Narayanan, Vineed; Venkatarathnam, G.
2018-03-01
Nitrogen-hydrocarbon mixtures are widely used as refrigerants in J-T refrigerators operating with mixtures, as well as in natural gas liquefiers. The Peng-Robinson equation of state has traditionally been used to simulate the above cryogenic process. Multi parameter Helmholtz energy equations are now preferred for determining the properties of natural gas. They have, however, been used only to predict vapour-liquid equilibria, and not vapour-liquid-liquid equilibria that can occur in mixtures used in cryogenic mixed refrigerant processes. In this paper the vapour-liquid equilibrium of binary mixtures of nitrogen-methane, nitrogen-ethane, nitrogen-propane, nitrogen-isobutane and three component mixtures of nitrogen-methane-ethane and nitrogen-methane-propane have been studied with the Peng-Robinson and the Helmholtz energy equations of state of NIST REFPROP and compared with experimental data available in the literature.
International Nuclear Information System (INIS)
Jiang Hui; Li Haoran; Wang Congmin; Tan Taijun; Han Shijun
2003-01-01
The isothermal and isobaric (vapour + liquid) equilibria for (2,2-dimethoxypropane + methanol) and (2,2-dimethoxypropane + acetone) measured with an inclined ebulliometer are presented. The experimental results are analysed using the UNIQUAC equation with the temperature-dependent binary parameters with satisfactory results. Isobaric (vapour + liquid) equilibria data for these systems at p=99.99 kPa are compared with the literature data. Experimental vapour pressure of 2,2-dimethoxypropane are also included
Vapour-liquid equilibria of the hard core Yukawa fluid
Smit, B.; Frenkel, D.
1991-01-01
Techniques which extend the range of applicability of the Gibbs ensemble technique for particles which interact with a hard core potential are described. The power of the new technique is demonstrated in a numerical study of the vapour-liquid coexistence curve of the hard core Yukawa fluid.
International Nuclear Information System (INIS)
Baseri, Hadi; Lotfollahi, Mohammad Nader
2011-01-01
Highlights: → Extended PR-EOS was presented for VLE of H 2 O/Salt/CO 2 systems at high pressure. → The proposed EPR-EOS is based upon contributions to the Helmholtz energy. → Born, Margules, and Debye-Huckel or mean spherical approximation terms were used. → Two different mixing rules Panagiotopoulos and Reid and Kwak and Mansoori (KM) were used. → A combination of KM mixing rule with DH term results more accurate VLE results. - Abstract: A modification of the extended Peng-Robinson equation of state (PR-EOS) is presented to describe the (vapour + liquid) equilibria of systems containing water and salts. The modification employs three additional terms including a Born term, a Margules term and two terms separately used for estimation of the long-range electrostatic interactions (the Debye-Huckel (DH) or the mean spherical approximation (MSA) terms). Effects of two mixing rules, first, the Panagiotopoulos and Reid mixing rule (PR) and, second, the Kwak and Mansoori mixing rule (KM), on the final values of VLE calculations are also investigated. The results show that the KM mixing rule is more appropriate than the PR mixing rule. The proposed equation of state is used to calculate the (vapour + liquid) equilibrium (VLE) of the systems containing (water + sodium sulphate + carbon dioxide) and (water + sodium chloride + carbon dioxide) at high pressure. The comparison of calculated results with the experimental data shows that a combination of KM mixing rule with the DH term results a more accurate VLE values.
Consistent vapour-liquid equilibrium data containing lipids
DEFF Research Database (Denmark)
Cunico, Larissa; Ceriani, Roberta; Sarup, Bent
Consistent physical and thermodynamic properties of pure components and their mixtures are important for process design, simulation, and optimization as well as design of chemical based products. In the case of lipids, it was observed a lack of experimental data for pure compounds and also...... for their mixtures in open literature, what makes necessary the development of reliable predictive models based on limited data. To contribute to the missing data, measurements of isobaric vapour-liquid equilibrium (VLE) data of three binary mixtures at two different pressures were performed at State University...
International Nuclear Information System (INIS)
Gutierrez, Jorge E.; Bejarano, Arturo; Fuente, Juan C. de la
2010-01-01
An apparatus based on a static-analytic method assembled in this work was utilized to perform high pressure (vapour + liquid) equilibria measurements with uncertainties estimated at 2 + 1-propanol), (CO 2 + 2-methyl-1-propanol), (CO 2 + 3-methyl-1-butanol), and (CO 2 + 1-pentanol) binary systems at temperatures of (313, 323, and 333) K, and at pressure range of (2 to 12) MPa. For all the (CO 2 + alcohol) systems, it was visually monitored to insure that there was no liquid immiscibility at the temperatures and pressures studied. The experimental results were correlated with the Peng-Robinson equation of state using the quadratic mixing rules of van der Waals with two adjustable parameters. The calculated (vapour + liquid) equilibria compositions were found to be in good agreement with the experimental values with deviations for the mol fractions <0.12 and <0.05 for the liquid and vapour phase, respectively.
International Nuclear Information System (INIS)
Lladosa, Estela; Monton, Juan B.; Burguet, MaCruz; Torre, Javier de la
2008-01-01
Isobaric (vapour + liquid + liquid) equilibria were measured for the (di-n-propyl ether + n-propyl alcohol + water) and (diisopropyl ether + isopropyl alcohol + water) system at 100 kPa. The apparatus used for the determination of (vapour + liquid + liquid) equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer couple to the boiling flask. The experimental data demonstrated the existence of a heterogeneous ternary azeotrope for both ternary systems. The (vapour + liquid + liquid) equilibria data were found to be thermodynamically consistent for both systems. The experimental data were compared with the estimation using UNIQUAC and NRTL models and the prediction of UNIFAC model
International Nuclear Information System (INIS)
Mokhtarani, Babak; Gmehling, Juergen
2010-01-01
(Vapour + liquid) equilibrium (VLE) data for the ternary systems (hexane + benzene), (hexane + cyclohexane), (benzene + cyclohexane), and (ethanol + water) with an ionic liquid as entrainer for extractive distillation were measured by headspace gas chromatography. As ionic liquids, 1-hexyl-3-methyl-imidazolium bis (trifluoromethyl-sulfonyl) imide [HMIM][BTI], 1-octyl-3-methyl-imidazolium bis (trifluoromethyl-sulfonyl) imide [OMIM][BTI], 1-octyl-3-methyl-imidazolium trifluoro-methanesulfonate [OMIM][OTF], and 1-butyl-3-methyl-imidazolium trifluoro-methanesulfonate [BMIM][OTF] were used. The experimental data show that the ionic liquids investigated have a great influence on the separation factors of the systems (hexane + benzene), (hexane + cyclohexane), and (benzene + cyclohexane). The experimental data were compared with the predicted results using mod. UNIFAC (Do). The predicted results are in good agreement with the experimental data.
Energy Technology Data Exchange (ETDEWEB)
Mokhtarani, Babak [Chemistry and Chemical Engineering Research Center of Iran, P.O. Box 14335-186, Tehran (Iran, Islamic Republic of); Gmehling, Juergen, E-mail: gmehling@tech.chem.uni-oldenburg.d [Carl von Ossietzky Universitaet Oldenburg, Technische Chemie, D-26111 Oldenburg (Germany)
2010-08-15
(Vapour + liquid) equilibrium (VLE) data for the ternary systems (hexane + benzene), (hexane + cyclohexane), (benzene + cyclohexane), and (ethanol + water) with an ionic liquid as entrainer for extractive distillation were measured by headspace gas chromatography. As ionic liquids, 1-hexyl-3-methyl-imidazolium bis (trifluoromethyl-sulfonyl) imide [HMIM][BTI], 1-octyl-3-methyl-imidazolium bis (trifluoromethyl-sulfonyl) imide [OMIM][BTI], 1-octyl-3-methyl-imidazolium trifluoro-methanesulfonate [OMIM][OTF], and 1-butyl-3-methyl-imidazolium trifluoro-methanesulfonate [BMIM][OTF] were used. The experimental data show that the ionic liquids investigated have a great influence on the separation factors of the systems (hexane + benzene), (hexane + cyclohexane), and (benzene + cyclohexane). The experimental data were compared with the predicted results using mod. UNIFAC (Do). The predicted results are in good agreement with the experimental data.
Energy Technology Data Exchange (ETDEWEB)
Gutierrez, Jorge E.; Bejarano, Arturo [Departamento de Ingenieria Quimica y Ambiental, Universidad Tecnica Federico Santa Maria, Avda. Espana 1680, Valparaiso (Chile); Fuente, Juan C. de la, E-mail: juan.delafuente@usm.c [Departamento de Ingenieria Quimica y Ambiental, Universidad Tecnica Federico Santa Maria, Avda. Espana 1680, Valparaiso (Chile); Centro Regional de Estudios en Alimentos Saludables, Blanco 1623, Valparaiso (Chile)
2010-05-15
An apparatus based on a static-analytic method assembled in this work was utilized to perform high pressure (vapour + liquid) equilibria measurements with uncertainties estimated at <5%. Complementary isothermal (vapour + liquid) equilibria results are reported for the (CO{sub 2} + 1-propanol), (CO{sub 2} + 2-methyl-1-propanol), (CO{sub 2} + 3-methyl-1-butanol), and (CO{sub 2} + 1-pentanol) binary systems at temperatures of (313, 323, and 333) K, and at pressure range of (2 to 12) MPa. For all the (CO{sub 2} + alcohol) systems, it was visually monitored to insure that there was no liquid immiscibility at the temperatures and pressures studied. The experimental results were correlated with the Peng-Robinson equation of state using the quadratic mixing rules of van der Waals with two adjustable parameters. The calculated (vapour + liquid) equilibria compositions were found to be in good agreement with the experimental values with deviations for the mol fractions <0.12 and <0.05 for the liquid and vapour phase, respectively.
A fresh look at the thermodynamic consistency of vapour-liquid equilibria data
International Nuclear Information System (INIS)
Wisniak, Jaime; Ortega, Juan; Fernández, Luis
2017-01-01
Highlights: • The thermodynamic consistency tests commonly used to evaluate VLE data are presented and discussed. • Advantages/disadvantages for each one of test are listed using actual examples. • All manuscripts should include information about VLE variables and test results. • In any case, the Herington test should not be used for VLE data evaluation. • Simultaneous application of several tests is recommended. - Abstract: Design of a separation unit requires real information about the phase equilibrium of the system being handled. Accurate equilibrium data allows the best design from a thermodynamic viewpoint and contributes to a better knowledge about the behaviour of fluids and their mixtures. The principles behind the concept of thermodynamic consistency are presented and discussed. The present state of the art shows that no definite test is available for insuring the quality of the measured values. The main available procedures for testing the consistency of vapour-liquid equilibrium (VLE) data at constant temperature or pressure are reviewed and analysed and recommendations provided for their proper use, for the presentation of VLE results, and also some possible means for determining their quality. Suitable examples are provided about the adequate use of the available tests and about their misuse.
Isothermal (vapour + liquid) equilibrium data for binary systems of (n-hexane + CO2 or CHF3)
International Nuclear Information System (INIS)
Williams-Wynn, Mark D.; Naidoo, Paramespri; Ramjugernath, Deresh
2016-01-01
Highlights: • (Static-analytic + static-synthetic) phase equilibrium measurements. • Binary VLE data for (CO 2 + n-hexane) and (trifluoromethane + n-hexane). • Thermodynamic models were fitted to the experimental data. • Liquid–liquid immiscibility occurred with (trifluoromethane + n-hexane) system. - Abstract: The (vapour + liquid) equilibrium (VLE) was measured for the (carbon dioxide + n-hexane) binary system at temperatures between T = (303.1 and 323.1) K. In addition, VLE and (vapour + liquid + liquid) equilibria (VLLE) were determined for the (trifluoromethane + n-hexane) binary system at temperatures between T = (272.9 and 313.3) K and pressures in the range of P = (1.0 to 5.7) MPa. Measurements were undertaken in a static-analytic apparatus, with verification of experimental values undertaken using a static-synthetic equilibrium cell to measure bubble point pressures at several compositions. The phase equilibrium results were modelled with the Peng–Robinson equation of state with the Mathias–Copeman alpha function, coupled with the Wong–Sandler mixing rules. Regression of the data was performed with the NRTL and the UNIQUAC activity coefficient models with the Wong–Sandler mixing rules, and the performance of the models was compared. Critical loci for both systems were estimated, using the calculation procedures of Ungerer et al. and Heidemann and Khalil. For the (trifluoromethane + n-hexane) system, liquid–liquid immiscibility was experienced at the lowest temperature measured (T = 272.9 K). At higher temperatures, no immiscibility was visible during the measurements; however, the models continued to predict a miscibility gap.
(Vapour + liquid) equilibria of the {1,1-difluoroethane (HFC-152a) + n-butane (HC-600)} system
International Nuclear Information System (INIS)
Im, Jihoon; Lee, Gangwon; Lee, Yong-Jin; Kim, Hwayong
2007-01-01
Binary (vapour + liquid) equilibrium data were obtained for the {1,1-difluoroethane (HFC-152a) + n-butane (HC-600)} system at temperatures from 313.15 K to 363.15 K. These experiments were carried out with a circulating-type apparatus with on-line gas chromatography. The experimental data were correlated well by Peng-Robinson equation of state using the Wong-Sandler mixing rules. This system shows positive azeotropic phase behaviour
Isobaric (vapour + liquid) equilibrium for N-methyl-2-pyrrolidone with branched alcohols
International Nuclear Information System (INIS)
Gnanakumari, P.; Venkatesu, P.; Hsieh, C.-T.; Rao, M.V. Prabhakara; Lee, M.-J.; Lin, Ho-mu
2009-01-01
The (vapour + liquid) equilibrium (VLE) and boiling temperature measurements have been determined at 95.3 kPa as a function of composition for the binary liquid mixtures of N-methyl-2-pyrrolidone (NMP) with branched alcohols using a Swietoslawski-ebulliometer. The branched alcohols include 2-propanol, 2-butanol, 2-methyl-l- propanol, 2-methyl-2-propanol, and 3-methyl-l-butanol. The experimental temperature-composition (T-x) results were used to estimate Wilson parameters and then used to calculate the equilibrium vapour compositions and the excess Gibbs free energy at T = 298.15 K. The experimental temperature-composition (T, x) results were correlated with the Wilson, the NRTL and the UNIQUAC models. The experimental results are interpreted in terms of intermolecular interactions between constituent molecules
Ruiz Beviá, Francisco; Gomis Yagües, Vicente; Asensi Steegmann, Juan Carlos; Font Escamilla, Alicia
2002-01-01
Poster enviado a Equifase 2002, VI Iberoamerican Conference on Phase Equilibria for Process Design, Foz de Iguazú (Brazil), October 12th to 16th, 2002. Many studies have been carried out in the heterogeneous azeotropic distillation field either by experiment or by simulation. The development of all these studies requires the use of sets of isobaric vapour–liquid–liquid equilibrium (VLLE) data. However, the number of ternary systems with experimental VLLE data is very limited, since it is d...
International Nuclear Information System (INIS)
Mohsen-Nia, M.; Memarzadeh, M.R.
2010-01-01
Isobaric (vapour + liquid) equilibrium measurements have been reported for the binary mixture of (1-pentanol + propionic acid) at (53.3 and 91.3) kPa. Liquid phase activity coefficients were calculated from the equilibrium data. The thermodynamic consistency of the experimental results was checked using the area test and direct test methods. According to these criteria, the measured (vapour + liquid) equilibrium results were found to be consistent thermodynamically. The obtained results showed a maximum boiling temperature azeotrope at both pressures studied. The measured equilibrium results were satisfactorily correlated by the models of Wilson, UNIQUAC, and NRTL activity coefficients. The results obtained indicate that the performance of the NRTL model is superior to the Wilson and UNIQUAC models for correlating the measured isobaric (vapour + liquid) equilibrium data.
International Nuclear Information System (INIS)
Radhamma, M.; Venkatesu, P.; Rao, M.V. Prabhakara; Prasad, D.H.L.
2007-01-01
Excess enthalpies (H E ), at ambient pressure and T = 298.15 K, have been measured by using a solution calorimeter for the binary liquid mixtures of dimethyl sulphoxide (DMSO) with ketones, as a function of composition. The ketones chosen in the present investigation were methyl ethyl ketone (MEK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The H E values are positive over the entire composition range for the three binary mixtures. Furthermore, the (vapour + liquid) equilibrium (VLE) was measured at 715 Torr for these mixtures, of different compositions, with the help of Swietoslawski-ebulliometer. The experimental temperature-mole fraction (t-x) data were used to compute Wilson parameters and then used to calculate the equilibrium vapour-phase compositions as well as the theoretical points for these binary mixtures. These Wilson parameters are used to calculate activity coefficients (γ) and these in turn to calculate excess Gibbs free energy (G E ). The intermolecular interactions and structural effects were analyzed on the basis of the measured and derived properties
International Nuclear Information System (INIS)
Nagata, Y.; Mizutani, K.; Miyamoto, H.
2011-01-01
Recently, it has been suggested that natural working fluids, such as CO 2 , hydrocarbons, and their mixtures, could provide a long-term alternative to fluorocarbon refrigerants. (Vapour + liquid) equilibrium (VLE) data for these fluids are essential for the development of equations of state, and for industrial process such as separation and refinement. However, there are large inconsistencies among the available literature data for (CO 2 + isobutane) binary mixtures, and therefore provision of reliable and new measurements with expanded uncertainties is required. In this study, we determined precise VLE data using a new re-circulating type apparatus, which was mainly designed by Akico Co., Japan. An equilibrium cell with an inner volume of about 380 cm 3 and two optical windows was used to observe the phase behaviour. The cell had re-circulating loops and expansion loops that were immersed in a thermostatted liquid bath and air bath, respectively. After establishment of a steady state in these loops, the compositions of the samples were measured by a gas chromatograph (GL Science, GC-3200). The VLE data were measured for CO 2 /propane and CO 2 /isobutane binary mixtures within the temperature range from 300 K to 330 K and at pressures up to 7 MPa. These data were compared with the available literature data and with values predicted by thermodynamic property models.
International Nuclear Information System (INIS)
Haghtalab, Ali; Espanani, Reza
2004-01-01
The cubic equation of state (CEOS) is a powerful method for calculation of (vapour + liquid) equilibrium (VLE) in polymer solutions. Using CEOS for both the vapour and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EOS approach. However, the traditional mixing rules are not appropriate to extend the CEOS to non-ideal mixtures such as polymer solutions. Several authors have applied the EOS/G E approach to predict (vapour + liquid) equilibria in polymer solutions, however, incorporating an appropriate excess Gibbs free energy for the new mixing rule is a major step. In this research, the NRTL-NRF model was extended in terms of volume fraction of polymer and solvent (instead of mole fraction), then equilibrium calculations were carried out using PRSV EOS and Wong-Sandler mixing rules. Using the adjustable parameters as a function of solution temperature, the NRTL-NRF model can be used as a predictive model. In comparison with NRTL model, the results of the new NRTL-NRF model show better accuracy
International Nuclear Information System (INIS)
Mulero, A.; Cuadros, F; Faundez, C.A.
1999-01-01
Vapour-liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour-liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state. Copyright (1999) CSIRO Australia
International Nuclear Information System (INIS)
Ye Kongmeng; Freund, Hannsjoerg; Sundmacher, Kai
2011-01-01
Highlights: → Phase behaviour modelling of H 2 O-MeOH-DME under pressurized CO 2 (anti-solvent) using PRWS. → PRWS-UNIFAC-PSRK has better performance than PRWS-UNIFAC-Lby in general. → Reliable to extend the VLE and VLLE phase behaviour from binary to multicomponent systems. → Successful prediction of the VLE and VLLE of binary, ternary, and quaternary systems. → Potential to apply the model for designing new DME separation process. - Abstract: The (vapour + liquid) equilibria (VLE) and (vapour + liquid + liquid) equilibria (VLLE) binary data from literature were correlated using the Peng-Robinson (PR) equation of state (EoS) with the Wong-Sandler mixing rule (WS). Two group contribution activity models were used in the PRWS: UNIFAC-PSRK and UNIFAC-Lby. The systems were successfully extrapolated from the binary systems to ternary and quaternary systems. Results indicate that the PRWS-UNIFAC-PSRK generally displays a better performance than the PRWS-UNIFAC-Lby.
Prediction of vapour-liquid equilibria for the kinetic study of processes based on synthesis gas
Energy Technology Data Exchange (ETDEWEB)
Di Serio, M.; Tesser, R.; Cozzolino, M.; Santacesaria, E. [Naples Univ., Napoli (Italy). Dept. of Chemistry
2006-07-01
Syngas is normally used in the production of a broad range of chemicals and fuels. In many of these processes multiphase reactors, gas-liquid or gas-liquid-solid are used. Kinetic studies in multiphase systems are often complicated by the non-ideal behaviour of reagents and/or products that are consistently partitioned between the liquid and the vapour phase. Moreover, as often kinetic data are collected in batch conditions for the liquid phase, activity coefficients of the partitioned components can consistently change during the time as a consequence of changing the composition of the reaction mixture. Therefore, it is necessary, in these cases, to known the vapor-liquid equilibria (VLE) in order to collect and to interpret correctly the kinetic data. The description of phase equilibria, at high pressures, is usually performed by means of an EOS (Equation of State) allowing the calculation of fugacity coefficients, for each component, in both phases and determining the partition coefficients but the EOS approach involves the experimental determination of the interaction parameters for all the possible binary system of the mixture. For multicomponent mixtures a complete experimental determination of vapourliquid equilibria is very hard, also considering the high pressure and temperatures used. Some predictive group contribution methods have been recently developed. In this paper, we will describe in detail the application of these methods to the methanol homologation, as an example, with the scope of determining more reliable kinetic parameters for this reaction. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Shen Chong [State Key Laboratory of Chemical Resource Engineering and College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029 (China); Ma Xiaoyan [College of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Lu Yingzhou [State Key Laboratory of Chemical Resource Engineering and College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029 (China); Li Chunxi, E-mail: Licx@mail.buct.edu.c [State Key Laboratory of Chemical Resource Engineering and College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029 (China)
2011-03-15
Vapour pressures were measured using a quasi-static ebulliometer for the binary mixture of (water + ethanol) containing one of three protonic ionic liquids (PIL), namely, mono-, di- or tri-ethanolammonium tetrafluoroborate, over the temperature range of (318.24 to 356.58) K at fixed PIL content of 0.30 in mass fraction. The vapour pressure data of the PIL-containing ternary systems were correlated using the NRTL equation with an overall root mean square deviation (RMSD) of 0.0092. The regressed NRTL parameters were used to predict the isobaric vapour liquid equilibria (VLE) for ternary systems (water + ethanol + PIL) at varying mass fraction of PIL and atmospheric pressure (101.3 kPa). It is shown that the effect of PILs on the VLE of the (water + ethanol) mixture follows the order: [HTEA][BF{sub 4}] > [HDEA][BF{sub 4}] > [HMEA][BF{sub 4}]. In addition, the relative volatilities of ethanol to water for pseudo-binary systems (water + ethanol + PIL) were calculated. The results indicate that the PILs studied can enhance the relative volatility of ethanol to water and even break the azeotropic behaviour of ethanol aqueous solution when PIL content is increased to a specified content.
Generalized method for calculation and prediction of vapour-liquid equilibria at high pressures
Energy Technology Data Exchange (ETDEWEB)
Drahos, J; Wichterle, I; Hala, E
1978-02-01
Following the approaches of K.C. Chao and J.D. Seader (see Gas Abstr. 18,24 (1962) Jan.) and B.I. Lee, J.H. Erbar, and W.C. Edmister (see Gas Abst. 29, 73-0331), the Czechoslovak Academy of Sciences developed a generalized method for prediction of vapor-liquid equilibria in hydrocarbon mixtures containing some nonhydrocarbon gases at high pressures. The method proposed is based on three equations: (1) a generalized equation of state for vapor-phase calculations; (2) a generalized expression for the pure-liquid fugacity coefficient; and (3) an activity coefficient expression based on a surface modification of the regular solution model. The equations used contain only one partially generalized binary parameter, which was evaluated from experimental K-value data. Researchers tested the proposed method by computing K-values and pressures in binary and multicomponent systems consisting of 13 hydrocarbons and 3 nonhydrocarbon gases. The results show that the method is applicable over a wide range of conditions with a degree of accuracy comparable with that of more complicated methods.
International Nuclear Information System (INIS)
Li Xuemei; Shen Chong; Li Chunxi
2012-01-01
Highlights ► Vapour pressures for six ternary systems containing an IL were measured. ► Components studied were water, ethanol, methanol, and alkanolammonium formates. ► The isobaric VLE were predicted using the fitted binary NRTL parameters. ► The ILs studied can generate a promising salt effect on VLE of azeotrope. ► [HMEA][HCOO] might be used as a potential entrainer in extractive distillation. - Abstract: Vapour pressures were measured using a quasi-static ebulliometer for the pseudo-binary mixtures of (water + ethanol), (water + methanol), and (methanol + ethanol) containing an alkanolammonium-based ionic liquid (IL), namely, mono-ethanolammonium formate ([HMEA][HCOO]) and di-ethanolammonium formate ([HDEA][HCOO]), respectively, with fixed IL mass fraction of 0.30 and over the temperature ranges of (292.12 to 371.13) K. The vapour pressures of the IL-containing ternary systems were favourably correlated using the NRTL model with an overall average absolute relative deviation (AARD) of 0.0082. Further, the salt effects of [HMEA][HCOO] and [HDEA][HCOO] on isobaric vapour liquid equilibria (VLE) of azeotrope and close boiling mixture, especially for the mixtures of (water + ethanol) and (methanol + ethanol), were investigated and compared with other ILs in terms of the x′–y phase diagrams predicted with the binary NRTL parameters. It is demonstrated that the relative volatilities of ethanol to water and ethanol to methanol are enhanced, and [HMEA][HCOO] might be used as a promising entrainer for the efficient separation of ethanol aqueous solution by special rectification.
International Nuclear Information System (INIS)
Gil-Hernandez, V.; Garcia-Gimenez, P.; Otin, S.; Artal, M.; Velasco, I.
2005-01-01
Isothermal (vapour + liquid) equilibria (VLE) at 313.15 K have been measured for liquid 1-propanol + dibromomethane, or + bromochloromethane or + 1,2-dichloroethane or + 1-bromo-2-chloroethane mixtures. The VLE data were reduced using the Redlich-Kister equation taking into consideration the vapour phase imperfection in terms of the 2nd molar virial coefficients. The excess molar Gibbs free energies of all the studied mixtures are positive and ranging from 794 J·mol -1 for (1-propanol + bromochloromethane) and 1052 J·mol -1 for (1-propanol + 1-bromo-2-chloroethane), at x = 0.5. The experimental results are compared with modified UNIFAC predictions
The Use of VMD Data/Model to Test Different Thermodynamic Models for Vapour-Liquid Equilibrium
DEFF Research Database (Denmark)
Abildskov, Jens; Azquierdo-Gil, M.A.; Jonsson, Gunnar Eigil
2004-01-01
Vacuum membrane distillation (VMD) has been studied as a separation process to remove volatile organic compounds from aqueous streams. A vapour pressure difference across a microporous hydrophobic membrane is the driving force for the mass transport through the membrane pores (this transport take...... place in vapour phase). The vapour pressure difference is obtained in VMD processes by applying a vacuum on one side of the membrane. The membrane acts as a mere support for the liquid-vapour equilibrium. The evaporation of the liquid stream takes place on the feed side of the membrane...... values; membrane type: PTFE/PP/PVDF; feed flow rate; feed temperature. A comparison is made between different thermodynamic models for calculating the vapour-liquid equilibrium at the membrane/pore interface. (C) 2004 Elsevier B.V. All rights reserved....
International Nuclear Information System (INIS)
Bejarano, Arturo; López, Pablo I.; Valle, José M. del; Fuente, Juan C. de la
2015-01-01
Highlights: • A new apparatus based on a static–analytic method was assembled in this work. • This work reports high-pressure VLE data of (E)-2-hexenal or hexanal + CO 2 + water. • Data includes (CO 2 + water) partition coefficients of (E)-2-hexenal and hexanal. • High separation factors from water (∼10 4 ) were found especially for (E)-2-hexenal. • The data were obtained at T = (313, 323, and 333) K and pressures from (8 to 19) MPa. - Abstract: A new apparatus based on a static–analytic method assembled in this work was utilised to perform high-pressure (vapour + liquid) equilibria measurements of aqueous ternary systems. This work includes values of isothermal partition coefficients between CO 2 and water of two apple aroma constituents, (E)-2-hexenal and hexanal. Additionally, this work reports new experimental (vapour + liquid) equilibria measurements for the ternary systems (CO 2 + (E)-2-hexenal + water) and (CO 2 + hexanal + water), at fixed liquid phase composition (600 mg · kg −1 ), at temperatures of (313, 323 and 333) K and at pressures from (8 to 19) MPa. Vapour liquid interphase was checked and monitored visually for all the systems studied in this work. No liquid immiscibility was observed at the composition, temperatures and pressures studied. In order to suggest reasonable operation conditions for fractionation of aromas with dense carbon dioxide, partition coefficients of the aroma compounds between CO 2 and water along with their separation factors from water were calculated. Partition coefficients of (E)-2-hexenal between CO 2 and water were in the range of (6 to 91) and where found to be near six times higher than those of hexanal (9 to 17). Very high separation factors from water were observed (∼10 4 ) especially for (E)-2-hexenal. The highest separation factor, for both compounds, was found at a temperature of 313 K and pressures from (12 to 14) MPa
International Nuclear Information System (INIS)
Guo, Hao; Gong, Maoqiong; Dong, Xueqiang; Wu, Jianfeng
2014-01-01
Highlights: • A new static analytical apparatus for vapour pressures and VLE data was designed. • The {R600a + R245fa} system was selected as a verification system. • Correlation of VLE data was made using PRvdWs and PRHVNRTL model. • Good agreement can be found with the literature data. - Abstract: A new static analytical apparatus for reliable vapour pressures and (vapour + liquid) equilibrium data of small-scale cell (≈150 mL) with internal stirrer and view windows was designed. In this work, the compositions of the phases were analyzed by a gas chromatograph connected on-line with TCD detectors. The operating pressure ranges from (0 to 3000) kPa, and the operating temperature range from (293 to 400) K. Phase equilibrium data for previously reported systems were first measured to test the credibility of the newly developed apparatus. The test included vapour pressure of 1,1,1,3,3-pentafluoropropane (R245fa) and isobutane (R600a), VLE of the (R600a + R245fa) system from T = (293.150 to 343.880) K. The measured VLE data are regressed with thermodynamic models using Peng–Robinson EoS with two different models, viz. the van der Waals mixing rule, and the Huron–Vidal mixing rule utilising the non-random two-liquid activity coefficient model. Thermodynamic consistency testing is also performed for the newly measured experimental data
International Nuclear Information System (INIS)
Lin, Dun-Yi; Tu, Chein-Hsiun
2012-01-01
Highlights: ► We report the VLE data at P = 101.3 kPa involving a cyclic ether. ► The activity coefficients of mixtures were obtained from modified Raoult’s law. ► The VLE data were correlated by four liquid activity coefficient models. ► The ternary VLE data were predicted from binary parameters of the four models. - Abstract: (Vapour + liquid) equilibrium (VLE) at P = 101.3 kPa have been determined for a ternary system (2-propanol + tetrahydropyran + 2,2,4-trimethylpentane) and its constituent binary systems (2-propanol + tetrahydropyran, 2-propanol + 2,2,4-trimethylpentane), and (tetrahydropyran + 2,2,4-trimethylpentane). Analysis of VLE data reveals that two binary systems (2-propanol + tetrahydropyran) and (2-propanol + 2,2,4-trimethylpentane) have a minimum boiling azeotrope. No azeotrope was found for the ternary system. The activity coefficients of liquid mixtures were obtained from the modified Raoult’s law and were used to calculate the reduced excess molar Gibbs free energy (g E /RT). Thermodynamic consistency tests were performed for all VLE data using the Van Ness direct test for the binary systems and the test of McDermott–Ellis as modified by Wisniak and Tamir for the ternary system. The VLE data of the binary mixtures were correlated using the three-suffix Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The models with their best-fitted interaction parameters of the binary systems were used to predict the ternary (vapour + liquid) equilibrium.
International Nuclear Information System (INIS)
Cunico, Larissa P.; Damaceno, Daniela S.; Matricarde Falleiro, Rafael M.; Sarup, Bent; Abildskov, Jens; Ceriani, Roberta; Gani, Rafiqul
2015-01-01
Highlights: • Novel VLE data for binary mixtures involving a partial acylglycerol (monocaprylin). • Use of a promising technique for measuring VLE/vapour pressure data (DSC technique). • The consistency of experimental data is analysed by a proposed methodology. • Regressed parameters are given for excess Gibbs thermodynamic models. • New regressed parameters are presented for UNIFAC to account for nonidealities. - Abstract: The Differential Scanning Calorimetry (DSC) technique is used for measuring isobaric (vapour + liquid) equilibria for two binary mixtures: {monocaprylin + palmitic acid (system 1) or methyl stearate (system 2)} at two different pressures P = (1.20 and 2.50) kPa. The obtained PTx data are correlated by Wilson, NRTL and UNIQUAC models. The original UNIFAC group contribution method is also considered and new binary interaction parameters for the main groups CH 2 , CCOO, OH and COOH are regressed, to account for the non-idealities found in these lipid systems. Established thermodynamic consistency tests are applied and attest the quality of the measured data. In terms of relevance of the selected components, system 1 can be found in the purification and deodorization steps during the production of edible oils, while, system 2 can be found in the purification steps of biodiesel. It should be noted that no such data could be found in the open literature, not only for the specific components selected but also for the combination of the classes of components considered; that is, acylglycerol plus fatty acid or fatty ester.
International Nuclear Information System (INIS)
Shen, Yanshu; Zheng, Danxing; Li, Xinru; Li, Yun
2013-01-01
Highlights: • Selected three formates that have relative perfect absorption performance for CO 2 . • Measured the VLE data of CO 2 + butyl, isobutyl, and amyl formates systems. • Correlated the VLE data by using PR EOS with two mixing rules and SRK EOS with one mixing rule. • Concluded amyl formate has potential research value as CO 2 physical absorbent. -- Abstract: In this work, three formates (butyl, isobutyl, and amyl formate) were considered as relative perfect CO 2 absorption performance based on the excess Gibbs function as the thermodynamics criterion. An online static-analytical method was used to measure the (vapour + liquid) equilibrium (VLE) data for the CO 2 + butyl, isobutyl, and amyl formates under the pressure of (0.2 to 6) MPa and the temperatures at a range from (283.15 to 343.15) K. Then the VLE data were correlated by Peng–Robinson (PR) equation of state (EOS) with classic mixing rule, PR EOS with Wong–Sandler (WS) mixing rule and Soave–Redlich–Kwong (SRK) EOS with classic mixing rule. It is shown that SRK EOS is comparatively appropriate for CO 2 + butyl formate binary system. Both PR EOS with classic mixing rule and SRK EOS can be used to correlate the binary systems of CO 2 + isobutyl, amyl formate. It is found that the solubility order of three formates for CO 2 from high to low is arranged as CO 2 + amyl formate > CO 2 + butyl formate > CO 2 + isobutyl formate, showing the system of CO 2 + amyl formate has the best absorption performance. By comparison, it indicates that formates have a greater solubility for CO 2 than acetates on the condition of the same temperature and pressure. In addition, the thermophysical properties, mole absorption and mass absorptive amount of several industrial absorbents were assessed and the absorption performance of amyl formate for CO 2 is better than other physical absorbents. Thus, the study concluded that amyl formate has potential research value as physical absorbent for CO 2 capture
International Nuclear Information System (INIS)
Khoiroh, Ianatul; Lee, Ming-Jer
2011-01-01
Highlights: → An autoclave apparatus was used for binary (vapour + liquid) equilibrium data measurement. → The studied systems are polyethylene glycol mono-4-nonylphenyl ether with alcohols. → The saturated pressure data were fitted accurately to the Antoine equation. → The NRTL model correlated well the phase equilibrium data. → The solvent activities have been calculated. - Abstract: Saturated pressures of three binary systems of oligomeric polyethylene glycol mono-4-nonylphenyl ether (PEGNPE) with methanol, ethanol, and 2-propanol have been measured by using an autoclave (vapour + liquid) equilibrium (VLE) apparatus at temperatures ranging from (340 to 455) K and the oligomer content ranging from 0.100 to 0.400 in mole fraction. With a given feed composition, equilibrium pressures were measured at various temperatures to obtain VLE data. The experimental data were fitted to the Antoine equation and also correlated with activity coefficient models, the NRTL and the UNIQUAC. The correlation results showed good agreement between the calculated values and the experimental data. In general, the NRTL model yielded better results. Additionally, the solvent activities were evaluated from the experimental results and were compared with those from the NRTL and the UNIQUAC models.
International Nuclear Information System (INIS)
Qian, Guo-fei; Liu, Wen; Wang, Li-tao; Wang, Dao-cai; Song, Hang
2013-01-01
Highlights: • We adopted a new extractive solvent “ethylene glycol” to separate the mixture. • We measured the VLE data of binary system n-propanol + ethylene glycol. • We reinforce the VLE data of binary system acetonitrile + ethylene glycol. • We predicted the VLE data for the ternary system successfully. -- Abstract: Experimental isobaric (Vapour + liquid) equilibrium (VLE) data at 101.3 kPa were determined for three binary systems, viz. {acetonitrile (1) + n-propanol (2)}, {acetonitrile (1) + ethylene glycol (3)} and {n-propanol (2) + ethylene glycol (3)} and for one ternary system {acetonitrile (1) + n-propanol (2) + ethylene glycol (3)}. The measurements were performed using an improved Rose equilibrium still. The VLE data of the binary systems passed thermodynamic consistency tests and were correlated by Wilson and NRTL models. Good results were achieved. The phase behaviour of the ternary system was predicted directly by the parameters of two models obtained from the experimental binary results. The results showed an excellent agreement with experimental values
International Nuclear Information System (INIS)
Sadeghi, Rahmat; Gholamireza, Afsaneh
2011-01-01
The apparent molar volumes and isentropic compressibility of glycine, L-alanine and L-serine in water and in aqueous solutions of (0.500 and 1.00) mol . kg -1 di-ammonium hydrogen citrate {(NH 4 ) 2 HCit} and those of (NH 4 ) 2 HCit in water have been obtained over the (288.15 to 313.15) K temperature range at 5 K intervals at atmospheric pressure from measurements of density and ultrasonic velocity. The apparent molar volume and isentropic compressibility values at infinite dilution of the investigated amino acids have been obtained and their variations with temperature and their transfer properties from water to aqueous solutions of (NH 4 ) 2 HCit have also been obtained. The results have been interpreted in terms of the hydration of the amino acids. In the second part of this work, water activity measurements by the isopiestic method have been carried out on the aqueous solutions of {glycine + (NH 4 ) 2 HCit}, {alanine + (NH 4 ) 2 HCit}, and {serine + (NH 4 ) 2 HCit} at T = 298.15 K at atmospheric pressure. From these measurements, values of vapour pressure, osmotic coefficient, activity coefficient and Gibbs free energy were obtained. The effect of the type of amino acids on the (vapour + liquid) equilibrium of the systems investigated has been studied. The experimental water activities have been correlated successfully with the segment-based local composition Wilson model. Furthermore, the thermodynamic behaviour of the ternary solutions investigated has been studied by using the semi-ideal hydration model and the linear concentration relations have been tested by comparing with the isopiestic measurements for the studied systems at T = 298.15 K.
Energy Technology Data Exchange (ETDEWEB)
Sadeghi, Rahmat, E-mail: rahsadeghi@yahoo.co [Department of Chemistry, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Gholamireza, Afsaneh [Department of Chemistry, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)
2011-02-15
The apparent molar volumes and isentropic compressibility of glycine, L-alanine and L-serine in water and in aqueous solutions of (0.500 and 1.00) mol . kg{sup -1} di-ammonium hydrogen citrate {l_brace}(NH{sub 4}){sub 2}HCit{r_brace} and those of (NH{sub 4}){sub 2}HCit in water have been obtained over the (288.15 to 313.15) K temperature range at 5 K intervals at atmospheric pressure from measurements of density and ultrasonic velocity. The apparent molar volume and isentropic compressibility values at infinite dilution of the investigated amino acids have been obtained and their variations with temperature and their transfer properties from water to aqueous solutions of (NH{sub 4}){sub 2}HCit have also been obtained. The results have been interpreted in terms of the hydration of the amino acids. In the second part of this work, water activity measurements by the isopiestic method have been carried out on the aqueous solutions of {l_brace}glycine + (NH{sub 4}){sub 2}HCit{r_brace}, {l_brace}alanine + (NH{sub 4}){sub 2}HCit{r_brace}, and {l_brace}serine + (NH{sub 4}){sub 2}HCit{r_brace} at T = 298.15 K at atmospheric pressure. From these measurements, values of vapour pressure, osmotic coefficient, activity coefficient and Gibbs free energy were obtained. The effect of the type of amino acids on the (vapour + liquid) equilibrium of the systems investigated has been studied. The experimental water activities have been correlated successfully with the segment-based local composition Wilson model. Furthermore, the thermodynamic behaviour of the ternary solutions investigated has been studied by using the semi-ideal hydration model and the linear concentration relations have been tested by comparing with the isopiestic measurements for the studied systems at T = 298.15 K.
Isothermal vapour-liquid equilibrium data for the binary systems of (CHF3 or C2F6) and n-heptane
International Nuclear Information System (INIS)
Williams-Wynn, Mark D.; Naidoo, Paramespri; Ramjugernath, Deresh
2016-01-01
Highlights: • Isothermal static-analytic and static-synthetic phase equilibrium measurements. • Binary VLE data for (CHF3 or C 2 F 6 ) + n-heptane. • Thermodynamic models were fitted to the experimental data. • Critical locus estimation for the systems. - Abstract: Isothermal vapour-liquid equilibrium (VLE) values for two binary systems; trifluoromethane and n-heptane at temperatures between T = (272.9 and 313.2) K, and hexafluoroethane and n-heptane at temperatures between T = (293.0 and 313.2) K were measured with a static-analytic apparatus. Bubble pressures at temperatures between T = (293.0 and 313.2) K, at several compositions, were also measured with a variable-volume static-synthetic apparatus. Vapour-liquid-liquid equilibrium (VLLE) was found to occur for certain isotherms for both of the systems. The PR EOS, with the Mathias-Copeman (MC) alpha function, combined with either the classical mixing rule or the Wong-Sandler (WS) mixing rule was used to correlate the experimental results. Either the NRTL or the UNIQUAC activity coefficient model was used within the WS mixing rule. The indirect extended scaling laws of Ungerer et al. were used to extrapolate critical loci from the experimental coexistence data, and the calculation procedure of Heidemann and Khalil was employed to calculate the mixture critical locus curves at temperatures close to the refrigerant critical temperatures. At lower temperatures on the mixture critical curve, gas-liquid critical points occurred, whereas, at higher temperatures, the critical points occurred along a liquid-liquid locus curve. The two systems were categorised according to the van Konynenburg and Scott classification.
International Nuclear Information System (INIS)
Wisniak, Jaime; Ortega, Juan; Fernández, Luis
2017-01-01
Highlights: • A critical analysis on the published data in JCT 102 (2016) 155–163, is carried out. • Different consistency tests are applied to the data used in this work for their thermodynamic evaluation. • It concludes by questioning the quality of the published data. - Abstract: The vapour-liquid equilibrium results reported by Zhang et al. [1] for the binary systems {methanol (1) + 2,2,3,3,4,4,5,5-octafluoro-1-pentanol (2)} and {2,2,3,3-tetrafluoro-1-propanol (1) + 2,2,3,3,4,4,5,5-octafluoro-1-pentanol (2)} have been analysed using the data evaluation methodology published recently [2] and found to be unreliable.
International Nuclear Information System (INIS)
Clara, Rene A.; Gomez Marigliano, Ana C.; Solimo, Horacio N.
2007-01-01
Density and viscosity measurements for pure chloroform and methyl isobutyl ketone at T = (283.15, 293.15, 303.15, and 313.15) K as well as for the binary system {x 1 chloroform + (1 - x 1 ) methyl isobutyl ketone} at the same temperatures were made over the whole concentration range. The experimental results were fitted to empirical equations, which permit the calculation of these properties over the whole concentration and temperature ranges studied. Data of the binary mixture were further used to calculate the excess molar volume and viscosity deviation. The (vapour + liquid) equilibrium (VLE) at T = 303.15 K for this binary system was also measured in order to calculate the activity coefficients and the excess molar Gibbs energy. This binary system shows no azeotrope and negative deviations from ideal behaviour. The excess or deviation properties were fitted to the Redlich-Kister polynomial relation to obtain their coefficients and standard deviations
International Nuclear Information System (INIS)
Sadeghi, Rahmat; Mahdavi, Adibeh
2012-01-01
Highlights: ► VLE and volumetry of binary and ternary [C 6 mim][Cl], MPM and EPM aqueous solutions. ► Constant a w lines show small negative deviation from the linear isopiestic relation. ► Solute–water interactions follow the order: EPM > MPM > [C 6 mim][Cl]. ► MPM and EPM have a very weak salting-out effect on [C 6 mim][Cl] aqueous solutions. - Abstract: (Vapour + liquid) equilibrium data (water activity, vapour pressure, osmotic coefficient, and activity coefficient) of binary aqueous solutions of 1-hexyl-3-methylimidazolium chloride ([C 6 mim][Cl]), methyl potassium malonate, and ethyl potassium malonate and ternary {[C 6 mim][Cl] + methyl potassium malonate} and {[C 6 mim][Cl] + ethyl potassium malonate} aqueous solutions were obtained through the isopiestic method at T = 298.15 K. These results reveal that the ionic liquid behaves as surfactant-like and aggregates in aqueous solutions at molality about 0.4 mol · kg −1 . The constant water activity lines of all the ternary systems investigated show small negative deviations from the linear isopiestic relation (Zdanovskii–Stokes–Robinson rule) derived using the semi-ideal hydration model. The density and speed of sound measurements were carried out on solutions of methyl potassium malonate and ethyl potassium malonate in water and of [C 6 mim][Cl] in aqueous solutions of 0.25 mol · kg −1 methyl potassium malonate and ethyl potassium malonate at T = (288.15 to 308.15) K at atmospheric pressure. From the experimental density and speed of sound data, the values of the apparent molar volume, apparent molar isentropic compressibility and excess molar volume were evaluated and from which the infinite dilution apparent molar volume and infinite dilution apparent molar isentropic compressibility were calculated at each temperature. Although, there are no clear differences between the values of the apparent molar volume of [C 6 mim][Cl] in pure water and in methyl potassium malonate or ethyl
International Nuclear Information System (INIS)
Domanska, Urszula; Lachwa, Joanna
2005-01-01
The (solid + liquid) equilibrium (SLE) of eight binary systems containing N-methyl-2-pyrrolidinone (NMP) with (2-propanone, or 2-butanone, or 2-pentanone, or 3-pentanone, or cyclopentanone, or 2-hexanone, or 4-methyl-2-pentanone, or 3-heptanone) were carried out by using a dynamic method from T = 200 K to the melting point of the NMP. The isothermal (vapour + liquid) equilibrium data (VLE) have been measured for three binary mixtures of NMP with 2-propanone, 3-pentanone and 2-hexanone at pressure range from p = 0 kPa to p = 115 kPa. Data were obtained at the temperature T = 333.15 K for the first system and at T = 373.15 K for the second two systems. The experimental results of SLE have been correlated using the binary parameters Wilson, UNIQUAC ASM and two modified NRTL equations. The root-mean-square deviations of the solubility temperatures for all the calculated values vary from (0.32 K to 0.68 K) and depend on the particular equation used. The data of VLE were correlated with one to three parameters in the Redlich-Kister expansion. Binary mixtures of NMP with (2-propanone, or 2-butanone, or 2-pentanone, or 3-pentanone, or cyclopentanone, or 2-hexanone, or 4-methyl-2-pentanone, or 3-heptanone) have been investigated in the framework of the modified UNIFAC (Do) model. The reported new interaction parameters for NMP-group (c-CONCH 3 ) and carbonyl group ( C=O) let the model consistently described a set of thermodynamic properties, including (solid + liquid) equilibrium (vapour + liquid) equilibrium, excess Gibbs energy and molar excess enthalpies of mixing. Our experimental and literature data of binary mixtures containing NMP and ketones were compared with the results of prediction with the modified UNIFAC (Do) model
International Nuclear Information System (INIS)
Atik, Zadjia
2008-01-01
(Vapour + liquid) equilibrium (VLE) of binary mixtures of (ethanol + α,α,α-trifluorotoluene), (benzene + α,α,α-trifluorotoluene), and (chloroform + α,α,α-trifluorotoluene) have been investigated at the pressure 101.4 kPa using the dynamic-ebulliometry method over the whole composition range. The correlated VLE phase diagrams were adequately described by means of NRTL and UNIQUAC thermodynamic models. Fair attractive energies in the first two systems are capable to yield azeotropes, while moderate repulsive energies in the later system make it zeotrope
Czech Academy of Sciences Publication Activity Database
Bernatová, Svatoslava; Wichterle, Ivan
2001-01-01
Roč. 180, 1-2 (2001), s. 235-245 ISSN 0378-3812 R&D Projects: GA ČR GA104/99/0136 Institutional research plan: CEZ:AV0Z4072921 Keywords : vapourůliquid equilibrium * experimental data * molar excess volume Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.217, year: 2001
Czech Academy of Sciences Publication Activity Database
Bernatová, Svatoslava; Pavlíček, Jan; Wichterle, Ivan
2011-01-01
Roč. 307, č. 1 (2011), s. 66-71 ISSN 0378-3812 R&D Projects: GA ČR GA104/07/0444 Institutional research plan: CEZ:AV0Z40720504 Keywords : vapor-liquid equilibrium * experimental data * prediction Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.139, year: 2011
Czech Academy of Sciences Publication Activity Database
Psutka, Štěpán; Wichterle, Ivan
2008-01-01
Roč. 264, 1-2 (2008) , s. 55-61 ISSN 0378-3812 R&D Projects: GA ČR(CZ) GA104/07/0444 Institutional research plan: CEZ:AV0Z40720504 Keywords : vapour–liquid equilibrium * experimental data * prediction Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.699, year: 2008
International Nuclear Information System (INIS)
Zhao, Yanxing; Dong, Xueqiang; Zhong, Quan; Gong, Maoqiong; Shen, Jun
2017-01-01
Highlights: • The vapour liquid equilibrium for ammonia + 1,1,1,2-tetrafluoroethane system was studied. • Measurements were based on vapour phase single recirculation method. • A positive azeotropic behaviour was exhibited at the experimental temperature range. - Abstract: To blend ammonia with some hydrofluorocarbons may give these mixed refrigerants lower flammability and global warming potential. In this paper, the isothermal vapour liquid equilibrium (VLE) of (ammonia + 1,1,1,2-tetrafluoroethane) system at temperatures ranging from (243.150 to 283.150) K are presented. Two models were employed to regress the experimental VLE results, namely the Peng–Robinson (PR) equation of state with the simple van der waals (VDW) mixing rule; the Peng–Robinson equation of state combined non-random two-liquid (NRTL) activity coefficient model with the modified Huron-Vidal one-order (MHV1) mixing rule. The maximum average absolute relative deviation of pressure (AARDp) and average absolute deviation of the vapour phase mole fraction (AADy) for PR-VDW are 0.56% and 0.010, respectively, while the maximum AARDp and AADy for PR-MHV1-NRTL are 0.27% and 0.014, respectively. Positive azeotropic behaviour was exhibited at each temperature investigated.
DEFF Research Database (Denmark)
Iliuta, Maria C.; Thomsen, Kaj; Rasmussen, Peter
2000-01-01
to aqueous salt systems containing non-electrolytes in order to demonstrate its ability in representing solid-liquid-vapour (SLV) equilibrium and thermal property data for these strongly non-ideal systems. The model requires only pure component and binary temperature-dependent interaction parameters....... The calculations are based on an extensive database consisting of salt solubility data in pure and mixed solvents, VLE data for solvent mixtures and mixed solvent-electrolyte systems and thermal properties for mixed solvent solutions. Application of the model to the methanol-water system in the presence of several...... ions (Na+, K+, NH4+, Cl-, NO3-, SO42-, CO2- and HCO3-) shows that the Extended UNIQUAC model is able to give an accurate description of VLE and SLE in ternary add quaternary mixtures, using the name set of binary interaction parameters. The capability of the model to predict accurately the phase...
International Nuclear Information System (INIS)
Li, Hao; Xia, Shuqian; Wu, Meng; Ma, Peisheng
2015-01-01
Highlights: • The two binary systems related to pyrolysis oil have been reported. • The VLE data were correlated well by the activity coefficient models. • The UNIFAC (Do) model was applied to predict the experimental VLE data. • The interaction parameter (ACOCH 3 –CH 3 COO) was obtained and proved to be reliable. • The obtained interaction parameters by NRTL model were used in the separation process design for the ternary mixture. - Abstract: Developing value-added chemicals from pyrolysis oil has been gaining increasing attention. Thus effective separation and purification of the pyrolysis oil are important and the phase equilibrium data are essential for the design and simulation of the processes. In this study, isobaric vapour–liquid equilibrium (VLE) for the two binary mixtures (butyl acetate + anisole) and (butyl acetate + guaiacol) have been determined at 101.33 kPa, a knowledge of which is essential for the separation of methoxy aromatic compounds (anisole and guaiacol) from biomass fast pyrolysis oil using butyl acetate as a solvent. All the experimental values were confirmed to be thermodynamically consistent using the van Ness method. The NRTL, UNIQUAC, and Wilson activity coefficient models were applied to regress the experimental values. The calculated results agreed well with the measured values. Furthermore, the results were calculated by the UNIFAC (Do) method (modified UNIFAC model) in which aromatic methoxyl is treated as a group (ACOCH 3 ). The new interaction parameter (ACOCH 3 –CH 3 COO) was obtained and proved to be reliable. Based on the preceding results, a feasible separation process for the ternary mixture (butyl acetate + anisole + guaiacol) has been designed to obtain the required products
International Nuclear Information System (INIS)
Larousse, B.; Lovera, P.; Borgard, J.M.; Roehrich, G.; Mokrani, N.; Maillault, C.; Doizi, D.; Dauvois, V.; Roujou, J.L.; Lorin, V.; Fauvet, P.; Carles, P.; Hartmann, J.M.
2009-01-01
In order to assess the choice of the sulphur-iodine thermochemical cycle for massive hydrogen production, a precise knowledge of the concentrations of the gaseous species (HI, I 2 , and H 2 O) in thermodynamic equilibrium with the liquid phase of the HI-I 2 -H 2 O ternary mixture is required, in a wide range of concentrations and for temperatures and pressures up to 300 degrees C and 50 bar. In the companion paper (Part 1) the experimental device was described, which enables the measurement of the total pressure and concentrations of the vapour phase (and thus the knowledge of the partial pressures of the different gaseous species) for the HI-I 2 -H 2 O mixture in the 20-140 degrees C range and up to 2 bar. This (Part 2) article describes the experimental device which enables similar measurements but now in the process domain. The results concerning concentrations in the vapour phase for the HI-I 2 -H 2 O initial mixture (with a global composition) in the 120-270 degrees C temperature range and up to 30 bar are presented. As previously, optical online diagnostics are used, based on recordings of infrared transmission spectra for HI and H 2 O and on UV/visible spectrometry for I 2 . The concentrations measured in the vapour phase are the first to describe the vapour composition under thermophysical conditions close to those of the distillation column. The experimental results are compared with a thermodynamic model and will help us to scale up and optimize the reactive distillation column we promote for the HI section of the sulphur-iodine cycle. (authors)
International Nuclear Information System (INIS)
Guo, Hao; Gong, Maoqiong; Dong, Xueqiang; Wu, Jianfeng
2012-01-01
Highlights: ► VLE data for the {R152a + R134} system were measured. ► The experiment is based on the static–analytic method. ► The VLE data were correlated using the PR–HV–NRTL model. ► A negative azeotropic behaviour was found. - Abstract: (Vapour + liquid) equilibrium (VLE) data for the {1,1-difluoroethane (R152a) + 1,1,2,2-Tetrafluoroethane (R134)} system were measured at T = (258.150 to 288.150) K. The experiment is based on a static–analytic method. Experimental data were correlated with the Peng–Robinson equation of state (PR EoS) and the Huron–Vidal (HV) mixing rule involving the NRTL activity coefficient model. The results show good agreement with experimental results for the binary system at each temperature. It was found that the system has a negative azeotropic behaviour within the temperature range measured here.
Czech Academy of Sciences Publication Activity Database
Bernatová, Svatoslava; Wichterle, Ivan
2001-01-01
Roč. 189, 1-2 (2001), s. 111-118 ISSN 0378-3812 R&D Projects: GA ČR GA104/99/0136 Institutional research plan: CEZ:AV0Z4072921 Keywords : vapour-liquid equilibrium * experimental data * molar excess volume Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.217, year: 2001
International Nuclear Information System (INIS)
Yang, Lixiang; Gong, Maoqiong; Guo, Hao; Dong, Xueqiang; Wu, Jianfeng
2015-01-01
Highlights: • VLE data for (R152a + R245fa) system were measured at temperatures. • The experiments were based on the static-analytic method. • VLE data were correlated using PR–vdWs and PR–HV–NRTL models. - Abstract: In this paper, (vapour + liquid) equilibrium (VLE) for the {1,1-difluoroethane (R152a) + 1,1,1,3,3-pentafluoropropane (R245fa)} system was determined by a static-analytical method at T = (323.150 to 353.150) K. Values of the VLE were correlated by the Peng–Robison equation of state (PR EoS) using two different models, the van der Waals (vdWs) mixing rule and the Huron–Vidal (HV) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The correlated results show good agreement with the experimental values. For the two models, the maximum average absolute deviations of the vapour phase mole fraction are 0.0034 and 0.0035, respectively.
Numerical computation of FCT equilibria by inverse equilibrium method
International Nuclear Information System (INIS)
Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki
1986-11-01
FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)
Directory of Open Access Journals (Sweden)
SLOBODAN P. SERBANOVIC
2000-12-01
Full Text Available The Kojima-Moon-Ochi (KMO thermodynamic consistency test of vapourliquid equilibrium (VLE measurements for 32 isothermal data sets of binary systems of various complexity was applied using two fitting equations: the Redlich-Kister equation and the Sum of Symmetrical Functions. It was shown that the enhanced reliability of the fitting of the experimental data can change the conclusions drawn on their thermodynamic consistency in those cases of VLE data sets that are estimated to be near the border of consistency.
International Nuclear Information System (INIS)
Subramoney, Shalendra Clinton; Nelson, Wayne Michael; Courtial, Xavier; Naidoo, Paramespri; Coquelet, Christophe; Richon, Dominique; Ramjugernath, Deresh
2015-01-01
Highlights: • Phase equilibrium data for propene and hexafluoropropylene. • Phase equilibrium data for propene and hexafluoropropylene oxide. • Systems exhibit pressure-maximum azeotropes. • Data well correlated by Peng–Robinson equation of state with the Wong–Sandler mixing rule. - Abstract: Isothermal (vapour + liquid) equilibrium data (P–x–y) are presented for the 1-propene 1,1,2,3,3,3-hexafluoro-1-propene and the 1-propene + 2,2,3-trifluoro-3-(trifluoromethyl)oxirane binary systems. Both binary systems were studied at five temperatures, ranging from (279.36 to 318.09) K, at pressures up to 2 MPa. The experimental (vapour + liquid) equilibrium data were measured using an apparatus based on the “(static + analytic)” method incorporating a single movable Rapid On-Line Sampler-Injector to sample the liquid and vapour phases at equilibrium. The expanded uncertainties are approximated on average as T = 0.07 K, 0.008 MPa, and 0.007 and 0.009 for the temperature, pressure, and the liquid and vapour mole fractions, respectively. A homogenous maximum-pressure azeotrope was observed for both binary systems at all temperatures studied. The experimental data were correlated with the Peng–Robinson equation of state using the Mathias–Copeman alpha function, paired with the Wong–Sandler mixing rule and the Non-Random Two Liquid activity coefficient model. The model provided satisfactory representation of the phase equilibrium data measured
Energy Technology Data Exchange (ETDEWEB)
Dong Xueqiang [Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190 (China); Graduate University of Chinese Academy of Sciences, Beijing 100039 (China); Gong Maoqiong, E-mail: gongmq@mail.ipc.ac.c [Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190 (China); Liu Junsheng [Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190 (China); Graduate University of Chinese Academy of Sciences, Beijing 100039 (China); Wu Jianfeng, E-mail: jfwu@mail.ipc.ac.c [Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190 (China)
2010-09-15
(Vapour + liquid) equilibrium (VLE) data for the binary systems of {l_brace}1,1,2,2-tetrafluoroethane (R134) + propane (R290){r_brace} and {l_brace}1,1,2,2-tetrafluoroethane (R134) + isobutane (R600a){r_brace} were measured with a recirculation method at the temperatures ranging from (263.15 to 278.15) K and (268.15 to 288.15) K, respectively. All of the data were correlated by the Peng-Robinson (PR) equation of state (EoS) with the Huron-Vidal (HV) mixing rules utilizing the non-random two-liquid (NRTL) activity coefficient model. Good agreement can be found between the experimental data and the correlated results. Azeotropic behaviour can be found at the measured temperature ranges for these two mixtures.
Improved grand canonical sampling of vapour-liquid transitions.
Wilding, Nigel B
2016-10-19
Simulation within the grand canonical ensemble is the method of choice for accurate studies of first order vapour-liquid phase transitions in model fluids. Such simulations typically employ sampling that is biased with respect to the overall number density in order to overcome the free energy barrier associated with mixed phase states. However, at low temperature and for large system size, this approach suffers a drastic slowing down in sampling efficiency. The culprits are geometrically induced transitions (stemming from the periodic boundary conditions) which involve changes in droplet shape from sphere to cylinder and cylinder to slab. Since the overall number density does not discriminate sufficiently between these shapes, it fails as an order parameter for biasing through the transitions. Here we report two approaches to ameliorating these difficulties. The first introduces a droplet shape based order parameter that generates a transition path from vapour to slab states for which spherical and cylindrical droplets are suppressed. The second simply biases with respect to the number density in a tetragonal subvolume of the system. Compared to the standard approach, both methods offer improved sampling, allowing estimates of coexistence parameters and vapor-liquid surface tension for larger system sizes and lower temperatures.
Isothermal vapour-liquid equilibria data of methanol + propan-2-OL ...
African Journals Online (AJOL)
methylpropan-2-ol binary mixtures are investigated at 333.15k, using gas chromatographic technique. ... The y-x plots reveals that the mixtures methanol + propan-2-ol and methanol +2-methylpropan-2-ol deviate strongly from ideal solution behaviour.
"Secrets" of High Pressure Phase Equilibrium Experiment.
Czech Academy of Sciences Publication Activity Database
Wichterle, Ivan
2005-01-01
Roč. 54, č. 11 (2005), s. 477-479 ISSN 0022-9830 Institutional research plan: CEZ:AV0Z40720504 Keywords : vapour-liquid equilibrium * experimental work Subject RIV: CF - Physical ; Theoretical Chemistry
Attractive evolutionary equilibria
Roorda, Berend; Joosten, Reinoud
2011-01-01
We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary dynamics. For instance, each attractive evolutionarily stable strategy is an attractive evolutionarily stable equilibrium for certain barycentric ray-projection dynamics, and vice versa.
Heat transfer in vapour-liquid flow of carbon dioxide
International Nuclear Information System (INIS)
Yagov, V.V.
2009-01-01
During the last decade a number of studies of boiling heat transfer in carbon dioxide notably increase. As a field of CO 2 practical using corresponds to high reduced pressures, and a majority of available experimental data on CO 2 flow boiling even in submillimetric channels relate to turbulent liquid flow regimes, a possibility arises to develop sufficiently general method for HTC predicting. Under the above conditions nucleate boiling occurs up to rather high flow quality, even in annular flow regime due to extremely small size of an equilibrium vapour bubble. This conclusion is in agreement with the available experimental data. The predicting equation for nucleate boiling heat transfer developed by the present author in 1988 is valid for any nonmetallic liquid. A contribution of forced convection in heat transfer is calculated according to the Petukhov et al. equation with correction factor, which accounted for an effect of velocity increase due to evaporation. This effect can be essential at relatively small heat fluxes and rather high mass flow rates. The Reynolds analogy and homogeneous model are used in order to account for the convective heat transfer augmentation in two-phase flow. Due to low ratio of liquid and vapour densities at high reduced pressures the homogeneous approximation of two-phase flow seems to be warranted. A total heat transfer coefficient is calculated as an interpolated value of boiling and convective HTCs. The experimental data on CO 2 flow boiling related to regimes before heated wall dryout incipience are in rather good agreement with the calculations. (author)
Some stable hydromagnetic equilibria
Energy Technology Data Exchange (ETDEWEB)
Johnson, J L; Oberman, C R; Kulsrud, R M; Frieman, E A [Project Matterhorn, Princeton University, Princeton, NJ (United States)
1958-07-01
We have been able to find and investigate the properties of equilibria which are hydromagnetically stable. These equilibria can be obtained, for example, by wrapping conductors helically around the stellarator tube. Systems with I = 3 or 4 are indicated to be optimum for stability purposes. In some cases an admixture of I = 2 fields can be advantageous for achieving equilibrium. (author)
Shevchenko, M.; Jak, E.
2017-12-01
The phase equilibria information on the Pb-Fe-O system is of practical importance for the improvement of the existing thermodynamic database of lead-containing slag systems (Pb-Zn-Fe-Cu-Si-Ca-Al-Mg-O). Phase equilibria of the Pb-Fe-O system have been investigated: (a) in air at temperatures between 1053 K and 1373 K (780 °C and 1100 °C); (b) in equilibrium with metallic lead at temperatures between 1053 K and 1373 K (780 °C and 1100 °C); and (c) at intermediate oxidation conditions for the liquid slag in equilibrium with two solids (spinel + magnetoplumbite), at temperatures between 1093 K and 1373 K (820 °C and 1100 °C). The high-temperature equilibration/quenching/electron probe X-ray microanalysis technique has been used to accurately determine the compositions of the phases in equilibrium in the system. The Pb and Fe concentrations in the phases were determined directly; preliminary thermodynamic modeling with FactSage was used to estimate the ferrous-to-ferric ratios and to present the results in the ternary diagram.
Energy Technology Data Exchange (ETDEWEB)
Ruffine, L.
2005-10-15
The need to develop and improve natural gas treatment processes is real. The petroleum industry usually uses separation processes which require phase equilibrium phenomena. Yet, the complexity of the phase equilibria involved results in a lack of data, which in turn limits the development of thermodynamic models. The first part of this work is devoted to experimental investigations for systems containing light hydrocarbons, methanol, water and acid gases. We present a new apparatus that was developed to measure vapor-liquid and vapor-liquid-liquid equilibria. It allowed us to obtain new phase composition data for the methanol-ethane binary system and different mixtures, and also to determine a part of the three phases equilibrium envelope of the same systems. In the second part of this work, we have developed a thermodynamic model based on the CPA equation of state. This choice may be justified by the presence of associating components like methanol, hydrogen sulfide and water in the systems. Such model is necessary for the design of gas treatment plants. Our model provides good results for phase equilibrium calculations for binaries systems without binary interaction parameter in many cases, and describes correctly the vapour-liquid and vapor-liquid-liquid equilibria for complex mixtures. (author)
Learning efficient correlated equilibria
Borowski, Holly P.; Marden, Jason R.; Shamma, Jeff S.
2014-01-01
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Learning efficient correlated equilibria
Borowski, Holly P.
2014-12-15
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents\\' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Learning to Play Efficient Coarse Correlated Equilibria
Borowski, Holly P.; Marden, Jason R.; Shamma, Jeff S.
2018-01-01
The majority of the distributed learning literature focuses on convergence to Nash equilibria. Coarse correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However
Czech Academy of Sciences Publication Activity Database
Pavlíček, Jan; Andresová, Adéla; Bogdanić, Grozdana; Wichterle, Ivan
2013-01-01
Roč. 344, APR 25 (2013), s. 59-64 ISSN 0378-3812 Institutional support: RVO:67985858 Keywords : vapour-liquid equilibrium * prediction * experimental data Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.241, year: 2013
Energy Technology Data Exchange (ETDEWEB)
Lewis, Derek
1969-07-01
A method is described for the estimation of equilibrium constants for aqueous systems at temperatures up to 374 deg C from entropy and free energy data for 25 deg C and data on the variation of heat capacity with temperature. Partial molal heat capacities of aqueous ions are estimated on the basis of the principle that, with suitably chosen standard states, the partial molal entropies of ions of a particular class at any given temperature are linearly related to the corresponding entropies at some reference temperature. The method suggested is compared with other methods, based on the Van't Hoff isobar and on an extension of the conventional scale of ionic free energy at 25 deg C, and the general dependence of aqueous equilibria on ionic heat capacity is considered.
High-pressure phase equilibria in the (carbon dioxide + 1-hexanol) system
International Nuclear Information System (INIS)
Secuianu, Catinca; Feroiu, Viorel; Geana, Dan
2010-01-01
(Vapour + liquid) equilibria (VLE) and (vapour + liquid + liquid) equilibria (VLLE) data for the (carbon dioxide + 1-hexanol) system were measured at (293.15, 303.15, 313.15, 333.15, and 353.15) K. Phase behaviour measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between (0.6 and 14.49) MPa. The Soave-Redlich-Kwong (SRK) equation of state (EOS) with classical van der Waals mixing rules (two-parameters conventional mixing rule, 2PCMR), was used in a semi-predictive approach, in order to represent the complex phase behaviour (critical curve, LLV line, isothermal VLE, LLE, and VLLE) of the system. The topology of phase behaviour is reasonably well predicted.
Selective-area vapour-liquid-solid growth of InP nanowires
International Nuclear Information System (INIS)
Dalacu, Dan; Kam, Alicia; Guy Austing, D; Wu Xiaohua; Lapointe, Jean; Aers, Geof C; Poole, Philip J
2009-01-01
A comparison is made between the conventional non-selective vapour-liquid-solid growth of InP nanowires and a novel selective-area growth process where the Au-seeded InP nanowires grow exclusively in the openings of a SiO 2 mask on an InP substrate. This new process allows the precise positioning and diameter control of the nanowires required for future advanced device fabrication. The growth temperature range is found to be extended for the selective-area growth technique due to removal of the competition between material incorporation at the Au/nanowire interface and the substrate. A model describing the growth mechanism is presented which successfully accounts for the nanoparticle size-dependent and time-dependent growth rate. The dominant indium collection process is found to be the scattering of the group III source material from the SiO 2 mask and subsequent capture by the nanowire, a process that had previously been ignored for selective-area growth by chemical beam epitaxy.
Selective-area vapour-liquid-solid growth of InP nanowires
Energy Technology Data Exchange (ETDEWEB)
Dalacu, Dan; Kam, Alicia; Guy Austing, D; Wu Xiaohua; Lapointe, Jean; Aers, Geof C; Poole, Philip J, E-mail: dan.dalacu@nrc-cnrc.gc.c [Institute for Microstructural Sciences, National Research Council of Canada, Ottawa, K1A 0R6 (Canada)
2009-09-30
A comparison is made between the conventional non-selective vapour-liquid-solid growth of InP nanowires and a novel selective-area growth process where the Au-seeded InP nanowires grow exclusively in the openings of a SiO{sub 2} mask on an InP substrate. This new process allows the precise positioning and diameter control of the nanowires required for future advanced device fabrication. The growth temperature range is found to be extended for the selective-area growth technique due to removal of the competition between material incorporation at the Au/nanowire interface and the substrate. A model describing the growth mechanism is presented which successfully accounts for the nanoparticle size-dependent and time-dependent growth rate. The dominant indium collection process is found to be the scattering of the group III source material from the SiO{sub 2} mask and subsequent capture by the nanowire, a process that had previously been ignored for selective-area growth by chemical beam epitaxy.
Partial Cooperative Equilibria: Existence and Characterization
Directory of Open Access Journals (Sweden)
Amandine Ghintran
2010-09-01
Full Text Available We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such set...... in OLG, learning in OLG and in games, optimal pricing of derivative securities, the impact of heterogeneity...
Pierce instability and bifurcating equilibria
International Nuclear Information System (INIS)
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
High-pressure fluid-phase equilibria: Experimental methods and systems investigated (2000-2004)
DEFF Research Database (Denmark)
Dohrn, Ralf; Peper, Stephanie; Fonseca, José
2010-01-01
As a part of a series of reviews, a compilation of systems for which high-pressure phase-equilibrium data were published between 2000 and 2004 is given. Vapor-liquid equilibria, liquid-liquid equilibria, vapor-liquid-liquid equilibria,solid-liquid equilibria, solid-vapor equilibria, solid-vapor-l...
Czech Academy of Sciences Publication Activity Database
Pavlíček, Jan; Bogdanić, Grozdana; Wichterle, Ivan
2012-01-01
Roč. 328, AUG 25 (2012), s. 61-68 ISSN 0378-3812 R&D Projects: GA ČR GA104/07/0444 Institutional support: RVO:67985858 Keywords : transesterification * vapour-liquid equilibrium * correlation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.379, year: 2012
International Nuclear Information System (INIS)
Garriga, R.; Perez, P.; Gracia, M.
2006-01-01
Vapour pressures of (tetrahydrofuran + 1,1,2,2-tetrachloroethane, or tetrachloroethene) at nine temperatures between T = 283.15 K and T = 323.15 K were measured by a static method. The reduction of the vapour pressures data to obtain activity coefficients and excess molar Gibbs energies was carried out by fitting the vapour pressure data to the Redlich-Kister polynomial according to Barker's method. Excess molar volumes were also measured at T 298.15 K. A comparative analysis about the thermodynamic behaviour of both systems is performed, in terms of hydrogen bonding and electron-donor-acceptor interactions, as well as the resonance effect in tetrachloroethene
Czech Academy of Sciences Publication Activity Database
Lísal, Martin; Smith, W. R.; Nezbeda, Ivo
2001-01-01
Roč. 181, 1-2 (2001), s. 127-146 ISSN 0378-3812 R&D Projects: GA ČR GA203/98/1446; GA AV ČR IAA4072712 Grant - others:NSERC(Ca) OGP1041 Institutional research plan: CEZ:AV0Z4072921 Keywords : computer simulations * mixtures * water Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.217, year: 2001
International Nuclear Information System (INIS)
Scheffel, J.
1982-04-01
Ideal MHD-equilibria for the toroidal EXTRAP configuration have been computed with an equilibrium code. The free-boundary prob- lem is solved by using the condition that the current density is proportional to r on a flux surface. It is found that the toroidal Z-pinch, initially induced in the central zero-field region of a transverse octupole field, drifts radially outwards producing an inverse -D shaped cross-section. The plasma current of this high- beta equilibrium may be increased if the plasma is pushed back by altering the external confining magnetic field as demonstrated. (Author)
Resurrecting Equilibria Through Cycles
DEFF Research Database (Denmark)
Barnett, Richard C.; Bhattacharya, Joydeep; Bunzel, Helle
equilibria because they asymptotically violate some economic restriction of the model. The literature has always ruled out such paths. This paper studies a pure-exchange monetary overlapping generations economy in which real balances cycle forever between momentary equilibrium points. The novelty is to show...... that segments of the offer curve that have been previously ignored, can in fact be used to produce asymptotically valid cyclical paths. Indeed, a cycle can bestow dynamic validity on momentary equilibrium points that had erstwhile been classified as dynamically invalid....
Multiple equilibria of divertor plasmas
International Nuclear Information System (INIS)
Vu, H.X.; Prinja, A.K.
1993-01-01
A one-dimensional, two-fluid transport model with a temperature-dependent neutral recycling coefficient is shown to give rise to multiple equilibria of divertor plasmas (bifurcation). Numerical techniques for obtaining these multiple equilibria and for examining their stability are presented. Although these numerical techniques have been well known to the scientific community, this is the first time they have been applied to divertor plasma modeling to show the existence of multiple equilibria as well as the stability of these solutions. Numerical and approximate analytical solutions of the present one-dimensional transport model both indicate that there exists three steady-state solutions corresponding to (1) a high-temperature, low-density equilibrium, (2) a low-temperature, high-density equilibrium, and (3) an intermediate-temperature equilibrium. While both the low-temperature and the high-temperature equilibria are stable, with respect to small perturbations in the plasma conditions, the intermediate-temperature equilibrium is physically unstable, i.e., any small perturbation about this equilibrium will cause a transition toward either the high-temperature or low-temperature equilibrium
Strong Nash Equilibria and the Potential Maimizer
van Megen, F.J.C.; Facchini, G.; Borm, P.E.M.; Tijs, S.H.
1996-01-01
A class of non cooperative games characterized by a `congestion e ect' is studied, in which there exists a strong Nash equilibrium, and the set of Nash equilibria, the set of strong Nash equilibria and the set of strategy pro les maximizing the potential function coincide.The structure of the class
Multiple equilibria in a simple elastocapillary system
Taroni, Michele; Vella, Dominic
2012-01-01
properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
Stackelberg equilibria and horizontal differentiation
Lambertini, Luca
1993-01-01
This paper proposes a taxonomy of the Stackelberg equilibria emerging from a standard game of horizontal differentiation à la Hotelling in which the strategy set of the sellers in the location stage is the real axis. Repeated leadership appears the most advantageous position. Furthermore, this endogenously yields vertical differentiation between products at equilibrium.
Brignole, Esteban Alberto
2013-01-01
Traditionally, the teaching of phase equilibria emphasizes the relationships between the thermodynamic variables of each phase in equilibrium rather than its engineering applications. This book changes the focus from the use of thermodynamics relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. Phase Equilibrium Engineering presents a systematic study and application of phase equilibrium tools to the development of chemical processes. The thermodynamic modeling of mixtures for process development, synthesis, simulation, design and
Learning to Play Efficient Coarse Correlated Equilibria
Borowski, Holly P.
2018-03-10
The majority of the distributed learning literature focuses on convergence to Nash equilibria. Coarse correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific coarse correlated equilibria. In this paper, we provide one such algorithm, which guarantees that the agents’ collective joint strategy will constitute an efficient coarse correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Uniqueness of Nash equilibria in a quantum Cournot duopoly game
International Nuclear Information System (INIS)
Sekiguchi, Yohei; Sakahara, Kiri; Sato, Takashi
2010-01-01
A quantum Cournot game whose classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties: (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.
Attractive evolutionary equilibria
Joosten, Reinoud A.M.G.; Roorda, Berend
2011-01-01
We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary
International Nuclear Information System (INIS)
Taschuk, M. T.; Tucker, R. T.; LaForge, J. M.; Beaudry, A. L.; Kupsta, M. R.; Brett, M. J.
2013-01-01
The vapour-liquid-solid glancing angle deposition (VLS-GLAD) process is capable of producing complex nanotree structures with control over azimuthal branch orientation and height. We have developed a thin film growth simulation including ballistic deposition, simplified surface diffusion, and droplet-mediated cubic crystal growth for the VLS-GLAD process using the Unreal TM Development Kit. The use of a commercial game engine has provided an interactive environment while allowing a custom physics implementation. Our simulation's output is verified against experimental data, including a volumetric film reconstruction produced using focused ion beam and scanning-electron microscopy (SEM), crystallographic texture, and morphological characteristics such as branch orientation. We achieve excellent morphological and texture agreement with experimental data, as well as qualitative agreement with SEM imagery. The simplified physics in our model reproduces the experimental films, indicating that the dominant role flux geometry plays in the VLS-GLAD competitive growth process responsible for azimuthally oriented branches and biaxial crystal texture evolution. The simulation's successful reproduction of experimental data indicates that it should have predictive power in designing novel VLS-GLAD structures
Taschuk, M. T.; Tucker, R. T.; LaForge, J. M.; Beaudry, A. L.; Kupsta, M. R.; Brett, M. J.
2013-12-01
The vapour-liquid-solid glancing angle deposition (VLS-GLAD) process is capable of producing complex nanotree structures with control over azimuthal branch orientation and height. We have developed a thin film growth simulation including ballistic deposition, simplified surface diffusion, and droplet-mediated cubic crystal growth for the VLS-GLAD process using the UnrealTM Development Kit. The use of a commercial game engine has provided an interactive environment while allowing a custom physics implementation. Our simulation's output is verified against experimental data, including a volumetric film reconstruction produced using focused ion beam and scanning-electron microscopy (SEM), crystallographic texture, and morphological characteristics such as branch orientation. We achieve excellent morphological and texture agreement with experimental data, as well as qualitative agreement with SEM imagery. The simplified physics in our model reproduces the experimental films, indicating that the dominant role flux geometry plays in the VLS-GLAD competitive growth process responsible for azimuthally oriented branches and biaxial crystal texture evolution. The simulation's successful reproduction of experimental data indicates that it should have predictive power in designing novel VLS-GLAD structures.
Phase equilibrium data for the ternary system (propane + chloroform + oryzanol)
International Nuclear Information System (INIS)
Correa, Fernanda V.; Comim, Sibele R.R.; Cesaro, Aline M. de; Rigo, Aline A.; Mazutti, Marcio A.; Hense, Haiko; Oliveira, J. Vladimir
2011-01-01
The compound oryzanol available in the rice bran (oriza sativa) is well known for its antioxidant activity. Phase equilibrium data involving oryzanol in compressed fluids, hardly found in the literature, are important to provide the basis for the extraction and fractionation processes. In this sense, the aim of this work is to report phase equilibrium measurements for the system (γ-oryzanol + chloroform) in compressed propane. Phase equilibrium experiments were performed using the static synthetic method (cloud points transition data) in a high-pressure variable-volume view cell in the temperature range of 303 K to 353 K, pressures up to 17 MPa, for oryzanol overall mass fractions of 2 wt%, 5 wt% and 10 wt% in (propane + chloroform) mixtures. A complex phase behaviour comprising vapour-liquid, liquid-liquid, vapour-liquid-liquid, solid-liquid, solid-liquid-liquid, solid-liquid-liquid-vapour transitions were visually observed for the system studied.
Phase equilibrium data for the ternary system (propane + chloroform + oryzanol)
Energy Technology Data Exchange (ETDEWEB)
Correa, Fernanda V.; Comim, Sibele R.R. [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil); Cesaro, Aline M. de; Rigo, Aline A.; Mazutti, Marcio A. [Department of Food Engineering, URI - Campus de Erechim, Av. Sete de Setembro, 1621, 99700-000 Erechim, RS (Brazil); Hense, Haiko [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil); Oliveira, J. Vladimir, E-mail: vladimir@uricer.edu.b [Department of Food Engineering, URI - Campus de Erechim, Av. Sete de Setembro, 1621, 99700-000 Erechim, RS (Brazil)
2011-01-15
The compound oryzanol available in the rice bran (oriza sativa) is well known for its antioxidant activity. Phase equilibrium data involving oryzanol in compressed fluids, hardly found in the literature, are important to provide the basis for the extraction and fractionation processes. In this sense, the aim of this work is to report phase equilibrium measurements for the system ({gamma}-oryzanol + chloroform) in compressed propane. Phase equilibrium experiments were performed using the static synthetic method (cloud points transition data) in a high-pressure variable-volume view cell in the temperature range of 303 K to 353 K, pressures up to 17 MPa, for oryzanol overall mass fractions of 2 wt%, 5 wt% and 10 wt% in (propane + chloroform) mixtures. A complex phase behaviour comprising vapour-liquid, liquid-liquid, vapour-liquid-liquid, solid-liquid, solid-liquid-liquid, solid-liquid-liquid-vapour transitions were visually observed for the system studied.
High-pressure Phase Equilibrium in the {Carbon Dioxide (1) + 1-Chloropropane (2)} Binary System.
Czech Academy of Sciences Publication Activity Database
Chorazewski, M.; Aim, Karel; Wichterle, Ivan; Jacquemin, J.; Polishuk, I.
2015-01-01
Roč. 91, č. 12 (2015), s. 165-171 ISSN 0021-9614 R&D Projects: GA AV ČR IAA400720710 Grant - others:BEMUSAC(XE) 72074-2002-04019 Institutional support: RVO:67985858 Keywords : vapour-liquid equilibrium * carbon dioxide * predictive modeling Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.196, year: 2015
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such set......Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria...... in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group...... membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include: determinacy in OLG with cash-in-advance constraints, income distribution and democracy...
Czech Academy of Sciences Publication Activity Database
Pavlíček, Jan; Bogdanić, Grozdana; Wichterle, Ivan
2017-01-01
Roč. 454, 25 DEC (2017), s. 111-115 ISSN 0378-3812 R&D Projects: GA ČR GA15-19542S Institutional support: RVO:67985858 Keywords : correlation * experimental data * polymer-solvent system Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Physical chemistry Impact factor: 2.473, year: 2016
(Vapour+liquid) equilibria of {xCH3Cl+(1-x)HCl} at temperatures (159.01 and 182.33) K
International Nuclear Information System (INIS)
Senra, A.M.P.; Fonseca, I.M.A.; Lobo, L.Q.
2005-01-01
VLE for (CH 3 Cl+HCl) has been experimentally determined at temperatures (159.01 and 182.33) K, using a static; method. The data were used to calculate the molar excess Gibbs energy at the two temperatures. The excess molar enthalpy estimated from the G m E values for the equimolar mixture is relatively large and negative: H m E =-(1011+/-318) J.mol -1 . The results have been compared with estimates from the chemical theory of solutions
Energy Technology Data Exchange (ETDEWEB)
Chiali-Baba Ahmed, Nouria [LATA2M, Laboratoire de Thermodynamique Appliquee et Modelisation Moleculaire, University AbouBekr Belkaid of Tlemcen, Post Office Box 119, Tlemcen 13000 (Algeria); Negadi, Latifa, E-mail: latifanegadi@yahoo.fr [LATA2M, Laboratoire de Thermodynamique Appliquee et Modelisation Moleculaire, University AbouBekr Belkaid of Tlemcen, Post Office Box 119, Tlemcen 13000 (Algeria); Mokbel, Ilham [LSA, Laboratoire des Sciences Analytiques, CNRS-UMR 5280, Universite Claude Bernard - Lyon I, 43, Bd du 11 Novembre 1918, Villeurbanne Cedex 69622 (France); Kaci, Ahmed Ait [Laboratoire de Thermodynamique et Modelisation Moleculaire, Universite des Sciences et de la Technologie Houari Boumediene, Post Office Box 32, El Alia 16111, Bab Ezzouar (Algeria); Jose, Jacques [LSA, Laboratoire des Sciences Analytiques, CNRS-UMR 5280, Universite Claude Bernard - Lyon I, 43, Bd du 11 Novembre 1918, Villeurbanne Cedex 69622 (France)
2012-01-15
Highlights: > Vapour pressures of sec-butylamine or cyclohexylamine and their aqueous solutions. > The investigated temperatures are 273 K and 363 K. > The (cyclohexylamine + water) mixture shows positive azeotropic behaviour. > The (sec-butylamine + water) or (cyclohexylamine + water) exhibit positive G{sup E}. - Abstract: The vapour pressures of (sec-butylamine + water), (cyclohexylamine + water) binary mixtures, and of pure sec-butylamine and cyclohexylamine components were measured by means of two static devices at temperatures between 293 (or 273) K and 363 K. The data were correlated with the Antoine equation. From these data, excess Gibbs functions (G{sup E}) were calculated for several constant temperatures and fitted to a fourth-order Redlich-Kister equation using the Barker's method. The (cyclohexylamine + water) system shows positive azeotropic behaviour for all investigated temperatures. The two binary mixtures exhibit positive deviations in G{sup E} for all investigated temperatures over the whole composition range.
Directory of Open Access Journals (Sweden)
Susial Pedro
2012-01-01
Full Text Available Vapour pressures of propyl acetate, isobutyl acetate and 2-propanol from 0.004 to 1.6 MPa absolute pressure and VLE data for the binary systems propyl acetate+ethanol, propyl acetate+2-propanol, isobutyl acetate+ethanol and isobutyl acetate+2-propanol at 0.15 MPa have been determined. The experimental VLE data were verified with the test of van Ness and the Fredenslund criterion. The propyl acetate+ethanol or +2-propanol binary systems have an azeotropic point at 0.15 MPa. The different versions of the UNIFAC and ASOG group contribution models were applied.
Czech Academy of Sciences Publication Activity Database
Psutka, Štěpán; Wichterle, Ivan
2005-01-01
Roč. 235, č. 1 (2005), s. 58-63 ISSN 0378-3812 R&D Projects: GA ČR(CZ) GA104/03/1555; GA AV ČR(CZ) KSK4040110 Institutional research plan: CEZ:AV0Z40720504 Keywords : VLE experimental data * prediction Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.478, year: 2005
Czech Academy of Sciences Publication Activity Database
Psutka, Štěpán; Wichterle, Ivan
2004-01-01
Roč. 220, č. 2 (2004), s. 161-165 ISSN 0378-3812 R&D Projects: GA ČR GA104/03/1555 Institutional research plan: CEZ:AV0Z4072921 Keywords : alcohol * ether * alkoxyalcohol Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.356, year: 2004
Czech Academy of Sciences Publication Activity Database
Pavlíček, Jan; Wichterle, Ivan
2012-01-01
Roč. 45, č. 1 (2012), s. 83-89 ISSN 0021-9614 R&D Projects: GA ČR GA104/07/0444 Institutional research plan: CEZ:AV0Z40720504 Keywords : alcohol * ketone * hydrocarbon Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.297, year: 2012
Energy Technology Data Exchange (ETDEWEB)
Tochigi, K. [Nihon Univ., Tokyo (Japan)
1998-08-05
The data on vapor-liquid equilibrium are basic data indispensable to the designing of a distillation process. The stage required for separation depends greatly upon the x-y curve, and the existence/nonexistence of an azeotropic point is also an important item to be checked. This paper describes the measurement of vapor-liquid equilibrium and liquid-liquid equilibrium, and then introduces reliable data on vapor-liquid equilibrium and parameters of an activity coefficient formula. For the prediction of vapor-liquid equilibrium, the ASOG, UNIFAC, and modified NIFAC, all being group contributive methods are utilized. The differences between these group contributive methods are based on the differences between the contributive items based on the differences in size of molecules influencing the activity coefficients and the expression of the group activity coefficient formula. The applicable number of groups of the ASOG is 43, while that of groups of the UNIFAC is 50. The modified UNIFAC covers 43 groups. The prediction of liquid-liquid equilibrium by using a group contributive method has little progressed since the of the results of the study of Magnussen et al. using the UNIFAC. 12 refs., 8 figs., 1 tab.
Computing Nash equilibria through computational intelligence methods
Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N.
2005-03-01
Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, to compute Nash equilibria of finite strategic games, as global minima of a real-valued, nonnegative function. An issue of particular interest is to detect more than one Nash equilibria of a game. The performance of the considered computational intelligence methods on this problem is investigated using multistart and deflection.
International Nuclear Information System (INIS)
Feber, R.D.; Lunsford, J.L.; Stark, W.A. Jr.
1976-05-01
An equilibrium analysis has been made of the fission-product cesium in the primary coolant loop of the high-temperature gas-cooled reactor (HTGR). The species distributions that result at equilibrium have been calculated for various conditions of reactor operation. The cesium species considered were the monomer, dimer, oxides, hydroxides, and the hydride. The effect of cesium sorption isotherms on graphite also was included in the analysis. During normal reactor operations, the abundant species of cesium were calculated to be elemental cesium, Cs, and the monomeric hydroxide, CsOH. Under most conditions of steam ingress, the abundant species was calculated to be CsOH. Cesium adsorbed onto graphite was stable under all steam-ingress conditions considered. Thermal transients above 1500 0 K were required for equilibrium transport of cesium from the core to the coolant. The analysis was carried out using the complex equilibrium code QUIL, designed and written with special emphasis on features that make it applicable to the fission-product problem
Chau, Nancy H.
2009-01-01
This paper presents a capability-augmented model of on the job search, in which sweatshop conditions stifle the capability of the working poor to search for a job while on the job. The augmented setting unveils a sweatshop equilibrium in an otherwise archetypal Burdett-Mortensen economy, and reconciles a number of oft noted yet perplexing features of sweatshop economies. We demonstrate existence of multiple rational expectation equilibria, graduation pathways out of sweatshops in complete abs...
International Nuclear Information System (INIS)
Hicks, H.R.; Dory, R.A.; Holmes, J.A.
1983-01-01
We illustrate in some detail a 2D inverse-equilibrium solver that was constructed to analyze tokamak configurations and stellarators (the latter in the context of the average method). To ensure that the method is suitable not only to determine equilibria, but also to provide appropriately represented data for existing stability codes, it is important to be able to control the Jacobian, tilde J is identical to delta(R,Z)/delta(rho, theta). The form chosen is tilde J = J 0 (rho)R/sup l/rho where rho is a flux surface label, and l is an integer. The initial implementation is for a fixed conducting-wall boundary, but the technique can be extended to a free-boundary model
International Nuclear Information System (INIS)
Taurino, A; Signore, M A
2015-01-01
In this work, the concurrent growth of InSe and In 2 O 3 nanostructures, obtained by thermal evaporation of InSe powders on Au-covered Si substrates, has been investigated by scanning and transmission electron microscopy techniques. The vapour-solid and Au catalytic vapour-liquid-solid growth mechanisms, responsible of the simultaneous development of the two different types of nanostructures, i.e. InSe wires and In 2 O 3 tulip-like structures respectively, are discussed in detail. The thermodynamic processes giving rise to the obtained morphologies and materials are explained. (paper)
Taurino, A.; Signore, M. A.
2015-06-01
In this work, the concurrent growth of InSe and In2O3 nanostructures, obtained by thermal evaporation of InSe powders on Au-covered Si substrates, has been investigated by scanning and transmission electron microscopy techniques. The vapour-solid and Au catalytic vapour-liquid-solid growth mechanisms, responsible of the simultaneous development of the two different types of nanostructures, i.e. InSe wires and In2O3 tulip-like structures respectively, are discussed in detail. The thermodynamic processes giving rise to the obtained morphologies and materials are explained.
Free-boundary perturbed MHD equilibria
International Nuclear Information System (INIS)
Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
Two-fluid equilibria with flow
International Nuclear Information System (INIS)
Steinhauer, L.
1999-01-01
The formalism is developed for flowing two-fluid equilibria. The equilibrium system is governed by a pair of second order partial differential equations for the magnetic stream function and the ion stream function plus a Bernoulli-like equation for the density. There are six arbitrary surface function. There are separate characteristic surfaces for each species, which are the guiding-center surfaces. This system is a generalization of the familiar Grad-Shafranov system for a single-fluid equilibrium without flow, which has only one equation and two arbitrary surface functions. In the case of minimum energy equilibria, the six surface functions take on particular forms. (author)
Inefficient equilibria in transition economy
Directory of Open Access Journals (Sweden)
Sergei Guriev
1999-01-01
Full Text Available The paper studies a general equilibrium in an economy where all market participants face a bid-ask spread. The spread may be caused by indirect business taxes, middlemen rent-seeking, delays in payments or liquidity constraints or price uncertainty. Wherever it comes from the spread causes inefficiency of the market equilibrium. We discuss some institutions that can decrease the inefficiency. One is second currency (barter exchange in the inter-firm transactions. It is shown that the general equilibrium in an economy with second currency is effective though is still different from Arrow–Debreu equilibrium. Another solution can be introduction of mutual trade credit. In the economy with trade credit there are multiple equilibria that are more efficient than original bid-ask spread but still not as efficient as Arrow–Debreu one, too. The implications for firms' integration and applicability to Russian economy are discussed.
A unifying approach to existence of Nash equilibria
Balder, E.J.
1997-01-01
An approach initiated in [4] is shown to unify results about the existence of (i) Nash equilibria in games with at most countably many players, (ii) Cournot-Nash equilibrium distributions for large, anonymous games, and (iii) Nash equilibria (both mixed and pure) for continuum games. A new, central
Nash Equilibria in Fisher Market
Adsul, Bharat; Babu, Ch. Sobhan; Garg, Jugal; Mehta, Ruta; Sohoni, Milind
Much work has been done on the computation of market equilibria. However due to strategic play by buyers, it is not clear whether these are actually observed in the market. Motivated by the observation that a buyer may derive a better payoff by feigning a different utility function and thereby manipulating the Fisher market equilibrium, we formulate the Fisher market game in which buyers strategize by posing different utility functions. We show that existence of a conflict-free allocation is a necessary condition for the Nash equilibria (NE) and also sufficient for the symmetric NE in this game. There are many NE with very different payoffs, and the Fisher equilibrium payoff is captured at a symmetric NE. We provide a complete polyhedral characterization of all the NE for the two-buyer market game. Surprisingly, all the NE of this game turn out to be symmetric and the corresponding payoffs constitute a piecewise linear concave curve. We also study the correlated equilibria of this game and show that third-party mediation does not help to achieve a better payoff than NE payoffs.
Collisionless current sheet equilibria
Neukirch, T.; Wilson, F.; Allanson, O.
2018-01-01
Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.
On the uniqueness of fully informative rational expectations equilibria
Peter DeMarzo; Costis Skiadas
1998-01-01
This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as r...
Energy Technology Data Exchange (ETDEWEB)
Martínez-Ruiz, F. J.; Blas, F. J., E-mail: felipe@uhu.es [Departamento de Física Aplicada, Universidad de Huelva, 21071 Huelva (Spain); Centro de Investigación de Física Teórica y Matemática, Universidad de Huelva, 21071 Huelva (Spain); Mendiboure, B. [Laboratoire des Fluides Complexes et leurs Réservoirs, UMR5150, Université de Pau et des Pays de l’Adour, B. P. 1155, Pau Cedex 64014 (France); Moreno-Ventas Bravo, A. I. [Centro de Investigación de Física Teórica y Matemática, Universidad de Huelva, 21071 Huelva (Spain); Departamento de Geología, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva (Spain)
2014-11-14
We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r{sub c} = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r{sub c} = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial
International Nuclear Information System (INIS)
Martínez-Ruiz, F. J.; Blas, F. J.; Mendiboure, B.; Moreno-Ventas Bravo, A. I.
2014-01-01
We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r c = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r c = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness
Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows
International Nuclear Information System (INIS)
Tasso, H.; Throumoulopoulos, G.N.
1997-12-01
It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)
Multiple equilibria in a simple elastocapillary system
Taroni, Michele
2012-09-28
We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
Phase equilibria and excess molar volumes of tetrahydrofuran (1) + deuterium oxide (2)
International Nuclear Information System (INIS)
Lejcek, P.; Matous, J.; Novak, J.P.; Pick, J.
1975-01-01
Vapour + liquid equilibrium at 313.15 and 333.15K, liquid + liquid equilibrium throughout the whole region of limited miscibility, and excess molar volumes at 298.15K have been studied for tetrahydrofuran + deuterium oxide. The mixtures show large positive deviations from Raoult's law and a closed loop of limited miscibility. The modified Redlich-Kister equation has been used for the correlation of the vapour + liquid equilibrium. The computation has been carried out according to a recently proposed procedure which makes it possible to obtain such constants of the correlation relation which are not inconsistent with physical reality, i.e. with the complete miscibility (partial delta 2 G/deltax 1 2 >0) under experimental conditions. Thermodynamic consistency was checked by the classical Redlich-Kister test and the one proposed by Ulrichson and Stevenson. Excess molar volumes are negative at all compositions with a point of inflexion in the water-rich region which indicates the extremes in partial molar volumes. (author)
Computation of Stackelberg Equilibria of Finite Sequential Games
DEFF Research Database (Denmark)
Bosanski, Branislav; Branzei, Simina; Hansen, Kristoffer Arnsfelt
2015-01-01
The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player~1 (the leader) first commits to a strategy that is publicly announced, then Player~2 (the follower) plays a best response to the leader's choice. We study Stackelberg equilibria in finite...... sequential (i.e., extensive-form) games and provide new exact algorithms, approximate algorithms, and hardness results for finding equilibria for several classes of such two-player games....
Determination of 3D Equilibria from Flux Surface Knowledge Only
International Nuclear Information System (INIS)
Mynick, H.E.; Pomphrey, N.
2001-01-01
We show that the method of Christiansen and Taylor, from which complete tokamak equilibria can be determined given only knowledge of the shape of the flux surfaces, can be extended to 3-dimensional equilibria, such as those of stellarators. As for the tokamak case, the given geometric knowledge has a high degree of redundancy, so that the full equilibrium can be obtained using only a small portion of that information
International Nuclear Information System (INIS)
Perfetti, E.
2006-11-01
Modelling fluid-rock interactions as well as mixing and unmixing phenomena in geological processes requires robust equations of state (EOS) which must be applicable to systems containing water, gases over a broad range of temperatures and pressures. Cubic equations of state based on the Van der Waals theory (e. g. Soave-Redlich-Kwong or Peng-Robinson) allow simple modelling from the critical parameters of the studied fluid components. However, the accuracy of such equations becomes poor when water is a major component of the fluid since neither association trough hydrogen bonding nor dipolar interactions are accounted for. The Helmholtz energy of a fluid may be written as the sum of different energetic contributions by factorization of partition function. The model developed in this thesis for the pure H 2 O and H 2 S considers three contributions. The first contribution represents the reference Van der Waals fluid which is modelled by the SRK cubic EOS. The second contribution accounts for association through hydrogen bonding and is modelled by a term derived from Cubic Plus Association (CPA) theory. The third contribution corresponds to the dipolar interactions and is modelled by the Mean Spherical Approximation (MSA) theory. The resulting CPAMSA equation has six adjustable parameters, which three represent physical terms whose values are close to their experimental counterpart. This equation results in a better reproduction of the thermodynamic properties of pure water than obtained using the classical CPA equation along the vapour-liquid equilibrium. In addition, extrapolation to higher temperatures and pressure is satisfactory. Similarly, taking into account dipolar interactions together with the SRK cubic equation of state for calculating molar volume of H 2 S as a function of pressure and temperature results in a significant improvement compared to the SRK equation alone. Simple mixing rules between dipolar molecules are proposed to model the H 2 O-H 2 S
Dudebout, Nicolas; Shamma, Jeff S.
2014-01-01
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
Dudebout, Nicolas
2014-12-15
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents\\' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
Helical axis stellarator equilibrium model
International Nuclear Information System (INIS)
Koniges, A.E.; Johnson, J.L.
1985-02-01
An asymptotic model is developed to study MHD equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two-dimensional generalized partial differential equation of the Grad-Shafranov type. A stellarator-expansion free-boundary equilibrium code is modified to solve the helical-axis equations. The expansion model is used to predict the equilibrium properties of Asperators NP-3 and NP-4. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift
Signaling equilibria in sensorimotor interactions.
Leibfried, Felix; Grau-Moya, Jordi; Braun, Daniel A
2015-08-01
Although complex forms of communication like human language are often assumed to have evolved out of more simple forms of sensorimotor signaling, less attention has been devoted to investigate the latter. Here, we study communicative sensorimotor behavior of humans in a two-person joint motor task where each player controls one dimension of a planar motion. We designed this joint task as a game where one player (the sender) possesses private information about a hidden target the other player (the receiver) wants to know about, and where the sender's actions are costly signals that influence the receiver's control strategy. We developed a game-theoretic model within the framework of signaling games to investigate whether subjects' behavior could be adequately described by the corresponding equilibrium solutions. The model predicts both separating and pooling equilibria, in which signaling does and does not occur respectively. We observed both kinds of equilibria in subjects and found that, in line with model predictions, the propensity of signaling decreased with increasing signaling costs and decreasing uncertainty on the part of the receiver. Our study demonstrates that signaling games, which have previously been applied to economic decision-making and animal communication, provide a framework for human signaling behavior arising during sensorimotor interactions in continuous and dynamic environments. Copyright © 2015 Elsevier B.V. All rights reserved.
Numerical calculation of axisymmetric non-neutral plasma equilibria
International Nuclear Information System (INIS)
Spencer, R.L.; Rasband, S.N.; Vanfleet, R.R.
1993-01-01
Efficient techniques for computing axisymmetric non-neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite-differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one-half Debye length to achieve the same accuracy
Guiding Center Equations in Toroidal Equilibria
International Nuclear Information System (INIS)
White, Roscoe; Zakharov, Leonid
2002-01-01
Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria
Equilibrium Constant as Solution to the Open Chemical Systems
Zilbergleyt, B.
2008-01-01
According to contemporary views, equilibrium constant is relevant only to true thermodynamic equilibria in isolated systems with one chemical reaction. The paper presents a novel formula that ties-up equilibrium constant and chemical system composition at any state, isolated or open as well. Extending the logarithmic logistic map of the Discrete Thermodynamics of Chemical Equilibria, this formula maps the system population at isolated equilibrium into the population at any open equilibrium at...
How hard is it to find extreme Nash equilibria in network congestion games?
Gassner, E.; Hatzl, J.; Krumke, S.O.; Sperber, H.; Woeginger, G.J.; Papadimitriou, C.; Zhang, S.
2008-01-01
We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach
Pura, Jose Luis; Periwal, Priyanka; Baron, Thierry; Jimenez, Juan
2018-06-05
The Vapour Liquid Solid (VLS) method is by far the most extended procedure for bottom-up nanowire growth. This method also allows for the manufacture of nanowire axial heterojunctions in a straightforward way. To do this, during the growth process the precursor gases are switched on/off to obtain the desired change in the nanowire composition. Using this technique axially heterostructured nanowires can be grown, which are crucial for the fabrication of electronic and optoelectronic devices. SiGe/Si nanowires are compatible with Complementary Metal Oxide Semiconductor (CMOS) technology, this improves their versatility and the possibility of integration with the current electronic technologies. Abrupt heterointerfaces are fundamental for the development and correct operation of electronic and optoelectronic devices. Unfortunately, VLS growth of SiGe/Si heterojunctions does not provide abrupt transitions because of the high solubility of group IV semiconductors in Au, with the corresponding reservoir effect that precludes the growth of sharp interfaces. In this work, we studied the growth dynamics of SiGe/Si heterojunctions based on already developed models for VLS growth. A composition map of the Si-Ge-Au liquid alloy is proposed to better understand the impact of the growing conditions on the nanowire growth process and the heterojunction formation. The solution of our model provides heterojunction profiles in good agreement with experimental measurements. Finally, the in-depth study of the composition map provides a practical approach to reduce drastically the heterojunction abruptness by reducing the Si and Ge concentrations in the catalyst droplet. This converges with previous approaches that use catalysts aiming to reduce the solubility of the atomic species. This analysis opens new paths to reduce the heterojunction abruptness using Au catalysts, but the model can be naturally extended to other catalysts and semiconductors. © 2018 IOP Publishing Ltd.
International Nuclear Information System (INIS)
Villamanan, Rosa M.; Martin, M. Carmen; Chamorro, Cesar R.; Villamanan, Miguel A.; Segovia, Jose J.
2006-01-01
(Vapour + liquid) equilibria data of (di-isopropyl ether + 1-butanol + benzene) (di-isopropyl ether + 1-butanol) and (1-butanol + benzene) have been measured at T = 313.15 K using an isothermal total pressure cell. Data reduction by Barker's method provides correlations for the excess molar Gibbs energy using the Margules equation for the binary systems and the Wohl expansion for the ternary. The Wilson, NRTL and UNIQUAC models have been applied successfully to both the binary and the ternary systems reported here
On Nash-Equilibria of Approximation-Stable Games
Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh
One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.
DEFF Research Database (Denmark)
Krøll, Annette Elisabeth; Marcussen, Lis
1997-01-01
An equilibrium equation for pure component adsorption is compared to experiments and to the vacancy solution theory. The investigated equilibrium equation is a special case of a model for prediction of multicomponent adsorption equilibria.The vacancy solution theory for multicomponent systems...... requires binary experimental data for determining the interaction parameters of the Wilson equation; thus a large number of experiments are needed. The multicomponent equilibria model which is investigated for single component systems in this work is based on pure component data only. This means...... that the requirement for experimental data is reduced significantly.The two adsorption models are compared, using experimental pure gas adsorption data found in literature. The results obtained by the models are in close agreement for pure component equilibria and they give a good description of the experimental data...
Computing Proper Equilibria of Zero-Sum Games
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Sørensen, Troels Bjerre
2007-01-01
We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game....
Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Johnson, J.L.; Dalhed, H.E.; Greene, J.M.
1978-07-01
Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given
High temperature phase equilibria and phase diagrams
Kuo, Chu-Kun; Yan, Dong-Sheng
2013-01-01
High temperature phase equilibria studies play an increasingly important role in materials science and engineering. It is especially significant in the research into the properties of the material and the ways in which they can be improved. This is achieved by observing equilibrium and by examining the phase relationships at high temperature. The study of high temperature phase diagrams of nonmetallic systems began in the early 1900s when silica and mineral systems containing silica were focussed upon. Since then technical ceramics emerged and more emphasis has been placed on high temperature
Solid-phase equilibria on Pluto's surface
Tan, Sugata P.; Kargel, Jeffrey S.
2018-03-01
Pluto's surface is covered by volatile ices that are in equilibrium with the atmosphere. Multicomponent phase equilibria may be calculated using a thermodynamic equation of state and, without additional assumptions, result in methane-rich and nitrogen-rich solid phases. The former is formed at temperature range between the atmospheric pressure-dependent sublimation and condensation points, while the latter is formed at temperatures lower than the sublimation point. The results, calculated for the observed 11 μbar atmospheric pressure and composition, are consistent with recent work derived from observations by New Horizons.
Accelerating Multiagent Reinforcement Learning by Equilibrium Transfer.
Hu, Yujing; Gao, Yang; An, Bo
2015-07-01
An important approach in multiagent reinforcement learning (MARL) is equilibrium-based MARL, which adopts equilibrium solution concepts in game theory and requires agents to play equilibrium strategies at each state. However, most existing equilibrium-based MARL algorithms cannot scale due to a large number of computationally expensive equilibrium computations (e.g., computing Nash equilibria is PPAD-hard) during learning. For the first time, this paper finds that during the learning process of equilibrium-based MARL, the one-shot games corresponding to each state's successive visits often have the same or similar equilibria (for some states more than 90% of games corresponding to successive visits have similar equilibria). Inspired by this observation, this paper proposes to use equilibrium transfer to accelerate equilibrium-based MARL. The key idea of equilibrium transfer is to reuse previously computed equilibria when each agent has a small incentive to deviate. By introducing transfer loss and transfer condition, a novel framework called equilibrium transfer-based MARL is proposed. We prove that although equilibrium transfer brings transfer loss, equilibrium-based MARL algorithms can still converge to an equilibrium policy under certain assumptions. Experimental results in widely used benchmarks (e.g., grid world game, soccer game, and wall game) show that the proposed framework: 1) not only significantly accelerates equilibrium-based MARL (up to 96.7% reduction in learning time), but also achieves higher average rewards than algorithms without equilibrium transfer and 2) scales significantly better than algorithms without equilibrium transfer when the state/action space grows and the number of agents increases.
Essays in general equilibrium theory
Konovalov, A.
2001-01-01
The thesis focuses on various issues of general equilibrium theory and can approximately be divided into three parts. The first part of the thesis studies generalized equilibria in the Arrow-Debreu model in the situation where the strong survival assumption is not satisfied. Chapter four deals with
DEFF Research Database (Denmark)
Cunico, Larissa P.; Damaceno, Daniela S.; Matricarde Falleiro, Rafael M.
2015-01-01
are applied and attest the quality of the measured data. In terms of relevance of the selected components, system 1 can be found in the purification and deodorization steps during the production of edible oils, while, system 2 can be found in the purification steps of biodiesel. It should be noted...
Czech Academy of Sciences Publication Activity Database
Bernatová, Svatoslava; Pavlíček, Jan; Wichterle, Ivan
2009-01-01
Roč. 278, 1-2 (2009), s. 129-134 ISSN 0378-3812 R&D Projects: GA ČR GA104/07/0444 Institutional research plan: CEZ:AV0Z40720504 Keywords : alcohol * ether * ketone Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.857, year: 2009
Analytic and numerical studies of Scyllac equilibrium
International Nuclear Information System (INIS)
Barnes, D.C.; Brackbill, J.U.; Dagazian, R.Y.; Freidberg, J.P.; Schneider, W.; Betancourt, O.; Garabedian, P.
1976-01-01
The results of both numerical and analytic studies of the Scyllac equilibria are presented. Analytic expansions are used to derive equilibrium equations appropriate to noncircular cross sections, and compute the stellarator fields which produce toroidal force balance. Numerical algorithms are used to solve both the equilibrium equations and the full system of dynamical equations in three dimensions. Numerical equilibria are found for both l = 1,0 and l= 1,2 systems. It is found that the stellarator fields which produce equilibria in the l = 1.0 system are larger for diffuse than for sharp boundary plasma profiles, and that the stability of the equilibria depends strongly on the harmonic content of the stellarator fields
Equilibria of perceptrons for simple contingency problems.
Dawson, Michael R W; Dupuis, Brian
2012-08-01
The contingency between cues and outcomes is fundamentally important to theories of causal reasoning and to theories of associative learning. Researchers have computed the equilibria of Rescorla-Wagner models for a variety of contingency problems, and have used these equilibria to identify situations in which the Rescorla-Wagner model is consistent, or inconsistent, with normative models of contingency. Mathematical analyses that directly compare artificial neural networks to contingency theory have not been performed, because of the assumed equivalence between the Rescorla-Wagner learning rule and the delta rule training of artificial neural networks. However, recent results indicate that this equivalence is not as straightforward as typically assumed, suggesting a strong need for mathematical accounts of how networks deal with contingency problems. One such analysis is presented here, where it is proven that the structure of the equilibrium for a simple network trained on a basic contingency problem is quite different from the structure of the equilibrium for a Rescorla-Wagner model faced with the same problem. However, these structural differences lead to functionally equivalent behavior. The implications of this result for the relationships between associative learning, contingency theory, and connectionism are discussed.
Computation of multi-region relaxed magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Hudson, S. R.; Lazerson, S. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Dewar, R. L.; Dennis, G.; Hole, M. J.; McGann, M.; Nessi, G. von [Plasma Research Laboratory, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)
2012-11-15
We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.; Aarts, D. G. A. L.; Howell, P. D.; Majumdar, A.
2017-01-01
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Three-dimensional plasma equilibrium near a separatrix
International Nuclear Information System (INIS)
Reiman, A.H.; Pomphrey, N.; Boozer, A.H.
1988-08-01
The limiting behavior of a general three-dimensional MHD equilibrium near a separatrix is calculated explicitly. No expansions in β or assumptions about island widths are made. Implications of the results for the numerical calculation of such equilibria, are discussed, as well as for issues concerning the existence of three-dimensional MHD equilibria. 16 refs., 2 figs
Equilibrium studies of helical axis stellarators
International Nuclear Information System (INIS)
Hender, T.C.; Carreras, B.A.; Garcia, L.; Harris, J.H.; Rome, J.A.; Cantrell, J.L.; Lynch, V.E.
1984-01-01
The equilibrium properties of helical axis stellarators are studied with a 3-D equilibrium code and with an average method (2-D). The helical axis ATF is shown to have a toroidally dominated equilibrium shift and good equilibria up to at least 10% peak beta. Low aspect ratio heliacs, with relatively large toroidal shifts, are shown to have low equilibrium beta limits (approx. 5%). Increasing the aspect ratio and number of field periods proportionally is found to improve the equilibrium beta limit. Alternatively, increasing the number of field periods at fixed aspect ratio which raises and lowers the toroidal shift improves the equilibrium beta limit
Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation
International Nuclear Information System (INIS)
Pletzer, A.; Zakharov, L.E.
1999-01-01
The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory
Thermodynamic Equilibria and Extrema Analysis of Attainability Regions and Partial Equilibria
Gorban, Alexander N; Kaganovich, Boris M; Keiko, Alexandre V; Shamansky, Vitaly A; Shirkalin, Igor A
2006-01-01
This book discusses mathematical models that are based on the concepts of classical equilibrium thermodynamics. They are intended for the analysis of possible results of diverse natural and production processes. Unlike the traditional models, these allow one to view the achievable set of partial equilibria with regards to constraints on kinetics, energy and mass exchange and to determine states of the studied systems of interest for the researcher. Application of the suggested models in chemical technology, energy and ecology is illustrated in the examples.
International Nuclear Information System (INIS)
Von Nessi, G T; Hole, M J
2014-01-01
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilized to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi et al 2012 J. Phys. A 46 185501). State-of-the-art results of using BEAST to study MAST equilibria are reviewed, with recent code advancements being systematically presented though out the manuscript. (paper)
The CHEASE code for toroidal MHD equilibria
Energy Technology Data Exchange (ETDEWEB)
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
The CHEASE code for toroidal MHD equilibria
International Nuclear Information System (INIS)
Luetjens, H.
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function Ψ. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs
Can markets compute equilibria?
Monroe , Hunter K
2009-01-01
Recent turmoil in financial and commodities markets has renewed questions regarding how well markets discover equilibrium prices, particularly when those markets are highly complex. A relatively new critique questions whether markets can realistically find equilibrium prices if computers cannot. For instance, in a simple exchange economy with Leontief preferences, the time required to compute equilibrium prices using the fastest known techniques is an exponential function of the number of goods. Furthermore, no efficient technique for this problem exists if a famous mathematical conjecture is
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
Adsorption analysis equilibria and kinetics
Do, Duong D
1998-01-01
This book covers topics of equilibria and kinetics of adsorption in porous media. Fundamental equilibria and kinetics are dealt with for homogeneous as well as heterogeneous particles. Five chapters of the book deal with equilibria and eight chapters deal with kinetics. Single component as well as multicomponent systems are discussed. In kinetics analysis, we deal with the various mass transport processes and their interactions inside a porous particle. Conventional approaches as well as the new approach using Maxwell-Stefan equations are presented. Various methods to measure diffusivity, such
Quantum equilibria for macroscopic systems
International Nuclear Information System (INIS)
Grib, A; Khrennikov, A; Parfionov, G; Starkov, K
2006-01-01
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered
Quantum equilibria for macroscopic systems
Energy Technology Data Exchange (ETDEWEB)
Grib, A [Department of Theoretical Physics and Astronomy, Russian State Pedagogical University, St. Petersburg (Russian Federation); Khrennikov, A [Centre for Mathematical Modelling in Physics and Cognitive Sciences Vaexjoe University (Sweden); Parfionov, G [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation); Starkov, K [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation)
2006-06-30
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered.
Extended Group Contribution Model for Polyfunctional Phase Equilibria
DEFF Research Database (Denmark)
Abildskov, Jens
of physical separation processes. In a thermodynamic sense, design requires detailed knowledge of activity coefficients in the phases at equilibrium. The prediction of these quantities from a minimum of experimental data is the broad scope of this thesis. Adequate equations exist for predicting vapor......Material and energy balances and equilibrium data form the basis of most design calculations. While material and energy balances may be stated without much difficulty, the design engineer is left with a choice between a wide variety of models for describing phase equilibria in the design......-liquid equilibria from data on binary mixtures, composed of structurally simple molecules with a single functional group. More complex is the situation with mixtures composed of structurally more complicated molecules or molecules with more than one functional group. The UNIFAC method is extended to handle...
On tokamak equilibria with a zero current or negative current central region
International Nuclear Information System (INIS)
Chu, M.S.; Parks, P.B.
2002-01-01
Several tokamak experiments have reported the development of a central region with vanishing currents (the current hole). The straightforward application of results from the work of Greene, Johnson and Weimer [Phys. Fluids 14, 671 (1971)] on a tokamak equilibrium to these plasmas leads to the apparent singularities in several physical quantities including the Shafranov shift and casts doubts on the existence of this type of equilibria. In this paper, the above quoted equilibrium theory is re-examined and extended to include equilibria with a current hole. It is shown that singularities can be circumvented and that equilibria with a central current hole do satisfy the magnetohydrodynamic equilibrium condition with regular behavior for all the physical quantities and do not lead to infinitely large Shafranov shifts. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization, i.e., no negative currents can be driven in the central region
Magnetic coordinates for equilibria with a continuous symmetry
International Nuclear Information System (INIS)
Dewar, R.L.; Monticello, D.A.; Sy, W.N.C.
1983-08-01
Magnetic coordinates for hydromagnetic equilibria are defined which treat toroidal and straight helical plasmas equivalently yet exploit the existence of a continuous symmetry to derive relations between various geometrical and physical quantities. This allows the number of equilibrium quantities which must be known to be reduced to a minimal, or primitive set. Practical formulae for various quantities required in hydromagnetic stability calculations (interchange, ballooning, and global) are given in terms of this primitive set
Phase equilibria and phase structures of polymer blends
International Nuclear Information System (INIS)
Chalykh, Anatolii E; Gerasimov, Vladimir K
2004-01-01
Experimental, methodical and theoretical studies dealing with phase equilibria and phase structures of polymer blends are generalised. The general and specific features of the change in solubility of polymers with changes in the molecular mass and copolymer composition and upon the formation of three-dimensional cross-linked networks are described. The results of the effect of the prehistory on the phase structure and the non-equilibrium state of polymer blends are considered in detail.
Jump conditions in transonic equilibria
International Nuclear Information System (INIS)
Guazzotto, L.; Betti, R.; Jardin, S. C.
2013-01-01
In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al.[Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that “standard” (low-β, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high-β, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches are described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large β, while they agree with the results obtained with the old implementation of FLOW in lower-β equilibria.
MHD equilibrium of heliotron J plasmas
International Nuclear Information System (INIS)
Suzuki, Yasuhiro; Nakamura, Yuji; Kondo, Katsumi; Nakajima, Noriyoshi; Hayashi, Takaya
2004-01-01
MHD equilibria of Heliotron J plasma are investigated by using HINT code. By assuming some profiles of the current density, effects of the net toroidal currents on the magnetohydrodynamics (MHD) equilibrium are investigated. If the rotational transform can be controlled by the currents, the generation of good flux surfaces is expected. In order to study equilibria with self-consistent bootstrap current, the boozer coordinates are constructed by converged HINT equilibrium as a preliminary study. Obtained spectra are compared with ones of VMEC code and both results are consistent. (author)
On financial equilibrium with intermediation costs
DEFF Research Database (Denmark)
Markeprand, Tobias Ejnar
2008-01-01
This paper studies the set of competitive equilibria in financial economies with intermediation costs. We consider an arbitrary dividend structure, which includes options and equity with limited liabilities.We show a general existence result and upper-hemi continuity of the equilibrium correspond......This paper studies the set of competitive equilibria in financial economies with intermediation costs. We consider an arbitrary dividend structure, which includes options and equity with limited liabilities.We show a general existence result and upper-hemi continuity of the equilibrium...
On generalized operator quasi-equilibrium problems
Kum, Sangho; Kim, Won Kyu
2008-09-01
In this paper, we will introduce the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which generalize the operator equilibrium problem due to Kazmi and Raouf [K.R. Kazmi, A. Raouf, A class of operator equilibrium problems, J. Math. Anal. Appl. 308 (2005) 554-564] into multi-valued and quasi-equilibrium problems. Using a Fan-Browder type fixed point theorem in [S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994) 493-519] and an existence theorem of equilibrium for 1-person game in [X.-P. Ding, W.K. Kim, K.-K. Tan, Equilibria of non-compact generalized games with L*-majorized preferences, J. Math. Anal. Appl. 164 (1992) 508-517] as basic tools, we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which includes operator equilibrium problems.
Kinetic description of linear theta-pinch equilibria
International Nuclear Information System (INIS)
Batchelor, D.B.; Davidson, R.C.
1975-01-01
Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (o/x=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bsub(z)sup(ext)esub(z). Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the th component distribution function (Hsub(perpendicular), Psub(theta), upsilonsub(z) depends on perpendicular energy H and canonical angular momentum Psub(theta), exclusively through the linear combination Hsub(perpendicular)-ωsub(j)Psub(theta), where ω;=const.=angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on Hsub(perpendicular)-ωsub(j)Psub(theta) in circumstances, where the density profile or magnetic field profile is specified. (author)
Shallow-water vortex equilibria and their stability
Energy Technology Data Exchange (ETDEWEB)
Plotka, H; Dritschel, D G, E-mail: hanna@mcs.st-andrews.ac.uk, E-mail: dgd@mcs.st-andrews.ac.uk [School of Mathematics and Statistics, University of St Andrews, North Haugh, St. Andrews KY16 9SS (United Kingdom)
2011-12-22
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L{sub D} called the 'Rossby deformation length' relating the strength of stratification to that of the background rotation rate. Specifically, L{sub D} = c/f where c={radical}gH is a characteristic gravity-wave speed, g is gravity (or 'reduced' gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call 'quasi-equilibria'. These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
International Nuclear Information System (INIS)
Scheffel, J.
1984-03-01
The linear Grad-Shafranov equation for a toroidal, axisymmetric plasma is solved analytically. Exact solutions are given in terms of confluent hyper-geometric functions. As an alternative, simple and accurate WKBJ solutions are presented. With parabolic pressure profiles, both hollow and peaked toroidal current density profiles are obtained. As an example the equilibrium of a z-pinch with a square-shaped cross section is derived.(author)
Variational-moment method for computing magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Lao, L.L.
1983-08-01
A fast yet accurate method to compute magnetohydrodynamic equilibria is provided by the variational-moment method, which is similar to the classical Rayleigh-Ritz-Galerkin approximation. The equilibrium solution sought is decomposed into a spectral representation. The partial differential equations describing the equilibrium are then recast into their equivalent variational form and systematically reduced to an optimum finite set of coupled ordinary differential equations. An appropriate spectral decomposition can make the series representing the solution coverge rapidly and hence substantially reduces the amount of computational time involved. The moment method was developed first to compute fixed-boundary inverse equilibria in axisymmetric toroidal geometry, and was demonstrated to be both efficient and accurate. The method since has been generalized to calculate free-boundary axisymmetric equilibria, to include toroidal plasma rotation and pressure anisotropy, and to treat three-dimensional toroidal geometry. In all these formulations, the flux surfaces are assumed to be smooth and nested so that the solutions can be decomposed in Fourier series in inverse coordinates. These recent developments and the advantages and limitations of the moment method are reviewed. The use of alternate coordinates for decomposition is discussed
Long-term Nash equilibria in electricity markets
International Nuclear Information System (INIS)
Pozo, David; Contreras, Javier; Caballero, Angel; de Andres, Antonio
2011-01-01
In competitive electricity markets, companies simultaneously offer their productions to obtain the maximum profits on a daily basis. In the long run, the strategies utilized by the electric companies lead to various long-term equilibria that can be analyzed with the appropriate tools. We present a methodology to find plausible long-term Nash equilibria in pool-based electricity markets. The methodology is based on an iterative market Nash equilibrium model in which the companies can decide upon their offer strategies. An exponential smoothing of the bids submitted by the companies is applied to facilitate the convergence of the iterative procedure. In each iteration of the model the companies face residual demand curves that are accurately modeled by Hermite interpolating polynomials. We introduce the concept of meta-game equilibrium strategies to allow companies to have a range of offer strategies where several pure and mixed meta-game Nash equilibria are possible. With our model it is also possible to model uncertainty or to generate price scenarios for financial models that assess the value of a generating unit by real options analysis. The application of the proposed methodology is illustrated with several realistic case studies. (author)
Averaged description of 3D MHD equilibrium
International Nuclear Information System (INIS)
Medvedev, S.Yu.; Drozdov, V.V.; Ivanov, A.A.; Martynov, A.A.; Pashekhonov, Yu.Yu.; Mikhailov, M.I.
2001-01-01
A general approach by S.A.Galkin et al. in 1991 to 2D description of MHD equilibrium and stability in 3D systems was proposed. The method requires a background 3D equilibrium with nested flux surfaces to generate the metric of a Riemannian space in which the background equilibrium is described by the 2D equation of Grad-Shafranov type. The equation can be solved then varying plasma profiles and shape to get approximate 3D equilibria. In the framework of the method both planar axis conventional stellarators and configurations with spatial magnetic axis can be studied. In the present report the formulation and numerical realization of the equilibrium problem for stellarators with planar axis is reviewed. The input background equilibria with nested flux surfaces are taken from vacuum magnetic field approximately described by analytic scalar potential
International Nuclear Information System (INIS)
Michielin, Eliane M.Z.; Rosso, Sibele R.; Franceschi, Elton; Borges, Gustavo R.; Corazza, Marcos L.; Oliveira, J. Vladimir; Ferreira, Sandra R.S.
2009-01-01
The aim of this work is to report phase equilibrium data for the binary systems (CO 2 + α-humulene) and (CO 2 + trans-caryophyllene), and for the ternary system (CO 2 + α-humulene + trans-caryophyllene). Results from literature show that α-humulene and trans-caryophyllene are the main compounds responsible for the anti-inflammatory and anti-allergic characteristics attributed to the medicinal plant Cordia verbenacea D.C., hence giving importance to the phase behaviour investigation performed in this work. Phase equilibrium experiments were performed in a high-pressure, variable-volume view cell over the temperature range of T = (303 to 343) K and pressures up to 20 MPa. (Liquid + liquid) and (vapour + liquid + liquid) equilibrium were observed at T = 303 K, while (vapour + liquid) phase transitions were verified to occur from T = (313 to 343) K, for all systems studied. Thermodynamic modelling was performed using the Peng-Robinson equation of state and the classical quadratic mixing rules, with a satisfactory agreement between experimental and calculated values
Energy Technology Data Exchange (ETDEWEB)
Michielin, Eliane M.Z.; Rosso, Sibele R [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil); Franceschi, Elton; Borges, Gustavo R; Corazza, Marcos L; Oliveira, J Vladimir [Department of Food Engineering, URI - Campus de Erechim, Av. Sete de Setembro, 1621, Erechim, RS, 99700-000 (Brazil); Ferreira, Sandra R.S. [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil)], E-mail: sandra@enq.ufsc.br
2009-01-15
The aim of this work is to report phase equilibrium data for the binary systems (CO{sub 2} + {alpha}-humulene) and (CO{sub 2} + trans-caryophyllene), and for the ternary system (CO{sub 2} + {alpha}-humulene + trans-caryophyllene). Results from literature show that {alpha}-humulene and trans-caryophyllene are the main compounds responsible for the anti-inflammatory and anti-allergic characteristics attributed to the medicinal plant Cordia verbenacea D.C., hence giving importance to the phase behaviour investigation performed in this work. Phase equilibrium experiments were performed in a high-pressure, variable-volume view cell over the temperature range of T = (303 to 343) K and pressures up to 20 MPa. (Liquid + liquid) and (vapour + liquid + liquid) equilibrium were observed at T = 303 K, while (vapour + liquid) phase transitions were verified to occur from T = (313 to 343) K, for all systems studied. Thermodynamic modelling was performed using the Peng-Robinson equation of state and the classical quadratic mixing rules, with a satisfactory agreement between experimental and calculated values.
Conditions for the Existence of Market Equilibrium.
Bryant, William D. A.
1997-01-01
Maintains that most graduate-level economics textbooks rarely mention the need for consumers to be above their minimum wealth position as a condition for market equilibrium. Argues that this omission leaves students with a mistaken sense about the range of circumstances under which market equilibria can exist. (MJP)
Equilibrium Selection in Games with Macroeconomic Complementarities
Kaarboe, Oddvar M.; Tieman, Alexander F.
1999-01-01
We apply the stochastic evolutionary approach of equilibrium selection tomacroeconomic models in which a complementarity at the macro level ispresent. These models often exhibit multiple Pareto-ranked Nash equilibria,and the best response-correspondence of an individual increases with ameasure of
Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations
International Nuclear Information System (INIS)
Agim, Y.Z.
1989-08-01
A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 -10
MINTEQ, Geochemical Equilibria in Ground Water
International Nuclear Information System (INIS)
Krupka, K.M.
1990-01-01
1 - Description of program or function: MINTEQ is a geochemical program to model aqueous solutions and the interactions of aqueous solutions with hypothesized assemblages of solid phases. It was developed for the Environmental Protection Agency to perform the calculations necessary to simulate the contact of waste solutions with heterogeneous sediments or the interaction of ground water with solidified wastes. MINTEQ can calculate ion speciation/solubility, adsorption, oxidation-reduction, gas phase equilibria, and precipitation/dissolution of solid phases. MINTEQ can accept a finite mass for any solid considered for dissolution and will dissolve the specified solid phase only until its initial mass is exhausted. This ability enables MINTEQ to model flow-through systems. In these systems the masses of solid phases that precipitate at earlier pore volumes can be dissolved at later pore volumes according to thermodynamic constraints imposed by the solution composition and solid phases present. The ability to model these systems permits evaluation of the geochemistry of dissolved traced metals, such as low-level waste in shallow land burial sites. MINTEQ was designed to solve geochemical equilibria for systems composed of one kilogram of water, various amounts of material dissolved in solution, and any solid materials that are present. Systems modeled using MINTEQ can exchange energy and material (open systems) or just energy (closed systems) with the surrounding environment. Each system is composed of a number of phases. Every phase is a region with distinct composition and physically definable boundaries. All of the material in the aqueous solution forms one phase. The gas phase is composed of any gaseous material present, and structurally distinct solid forms a separate phase. 2 - Method of solution: MINTEQ applies the fundamental principles of thermodynamics to solve geochemical equilibria from a set of mass balance equations, one for each component. Because the
Energy Technology Data Exchange (ETDEWEB)
Sultana, Jenifar; Das, Anindita [Centre for Research in Nanoscience and Nanotechnology (CRNN), Kolkata 700098 (India); Das, Avishek [Department of Electronic Science, University of Calcutta, Kolkata 700009 (India); Saha, Nayan Ranjan [Department of Polymer Science and Technology, University of Calcutta, Kolkata 700009 (India); Karmakar, Anupam [Department of Electronic Science, University of Calcutta, Kolkata 700009 (India); Chattopadhyay, Sanatan, E-mail: scelc@caluniv.ac.in [Department of Electronic Science, University of Calcutta, Kolkata 700009 (India)
2016-08-01
In this work, the CuO nano-powder has been synthesized by employing chemical bath deposition technique for its subsequent use to grow ultrathin film (20 nm) of p-CuO on n-Si substrate for the fabrication of p-CuO/n-Si hetero-junction diodes. The thin CuO film has been grown by employing vapour-liquid-solid method. The crystalline structure and chemical phase of the film are characterized by employing field-emission scanning electron microscopy and X-ray diffraction studies. Chemical stoichiometry of the film has been confirmed by using energy dispersive X-ray spectroscopy. The potential for photovoltaic applications of such films is investigated by measuring the junction current-voltage characteristics and by extracting the relevant parameters such as open circuit photo-generated voltage, short circuit current density, fill-factor and energy conversion efficiency. - Highlights: • Synthesis of CuO nano-powder by CBD method • Growth of ultra-thin film of CuO by employing VLS method for the first time • Physical and electrical characterization of such films for photovoltaic applications • Estimation of energy conversion efficiency of the p-CuO/n-Si p-n junction solar cell.
Stability of the n = 1 internal kink mode in equilibria with flows
International Nuclear Information System (INIS)
Aydemir, A.Y.; Waelbroeck, F.L.
1996-01-01
Stabilizing influence of mass flows, either directly or through their shearing action, on various modes is now generally recognized. Here we examine linear and nonlinear stability of the n = 1 internal kink mode in equilibria with toroidal rotation, using our nonlinear, initial-value MHD code CTD, which can be used to generate self-consistent equilibria with flows in arbitrary geometries. It is well known that equilibrium mass flows introduce complications in determination of MHD equilibria and their stability properties, such as the loss of self-adjointness and an increase in the number of conditions required to uniquely determine the equilibria. Thus, even with purely toroidal flows, an implicit statement about the equation of state is needed, in addition to a knowledge of the magnetic field and velocity profiles; rotation in an adiabatic plasma leads to a different equilibrium than, for example, in an isothermal one, with possibly quite different stability properties. We find that the expected stabilizing influence of toroidal rotation on n = 1 is generally absent in adiabatically generated equilibria in which, of all the relevant thermodynamic variables, only the specific entropy is a flux function, s = s (ψ). Fortunately, physically more relevant isothermal case where the temperature is constant on flux surfaces, T = T(ψ), has more favorable stability characteristics. On the other hand, an inconsistent but common practice of ignoring density perturbations, a benign omission for static equilibria, leads to overly optimistic results when equilibrium flows axe present, predicting stability when there may not be any. The crucial role played by the equation of state in determining equilibrium raises questions regarding the role of parallel transport in stability calculations; this and other nonideal effects, along with the role of plasma β vs. the rotational β, and nonlinear stability when the mode is pushed beyond marginality, will be discussed
Social Interactions under Incomplete Information: Games, Equilibria, and Expectations
Yang, Chao
My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter "A Tobit Model with Social
Gas hydrate phase equilibria measurement techniques and phase rule considerations
International Nuclear Information System (INIS)
Beltran, Juan G.; Bruusgaard, Hallvard; Servio, Phillip
2012-01-01
Highlights: → Inconsistencies found in hydrate literature. → Clarification to the number of variables needed to satisfy and justify equilibrium data. → Application of phase rule to mixed hydrate systems. → Thermodynamically consistent format to present data. - Abstract: A brief review of the Gibbs phase rule for non-reacting systems and its correct application to clathrate hydrates is presented. Clarification is provided for a common mistake found in hydrate phase-equilibria literature, whereby initial compositions are used as intensive variables to satisfy the Gibbs phase rule instead of the equilibrium values. The system of (methane + carbon dioxide + water) under (hydrate + liquid + vapor) equilibrium is used as a case study to illustrate key points and suggestions to improve experimental techniques are proposed.
A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry
Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew
2012-01-01
In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…
Construction of Subgame-Perfect Mixed Strategy Equilibria in Repeated Games
Berg, Kimmo; Schoenmakers, Gijsbertus
2017-01-01
This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring.We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called
On pure-strategy Nash equilibria in price-quantity games
Bos, I.; Vermeulen, A.J.
2015-01-01
This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms set both prices and quantities. Existence is proved for a broad and natural class of price-quantity games. With differentiated products, the equilibrium outcome is similar to
Efstathiou, K; Sadovskii, DA; Zhilinskii, BI
2004-01-01
We study relative equilibria ( RE) of a nonrigid molecule, which vibrates about a well-defined equilibrium configuration and rotates as a whole. Our analysis unifies the theory of rotational and vibrational RE. We rely on the detailed study of the symmetry group action on the initial and reduced
Chemical exchange equilibria in isotope separation. Part I : Evaluation of separation factors
International Nuclear Information System (INIS)
Dave, S.M.
1980-01-01
The theory of chemical exchange equilibria as applied to the isotope separation processes and the isotope effects on equilibrium constants of different exchange reactions has come a long way since its inception by Urey and Rittenberg. An attempt has been made to bring relevant information together and present a unified approach to isotopic chemical exchange equilibrium constant evaluation and its implications to separation processes. (auth.)
Energy Technology Data Exchange (ETDEWEB)
Perfetti, E
2006-11-15
Modelling fluid-rock interactions as well as mixing and unmixing phenomena in geological processes requires robust equations of state (EOS) which must be applicable to systems containing water, gases over a broad range of temperatures and pressures. Cubic equations of state based on the Van der Waals theory (e. g. Soave-Redlich-Kwong or Peng-Robinson) allow simple modelling from the critical parameters of the studied fluid components. However, the accuracy of such equations becomes poor when water is a major component of the fluid since neither association trough hydrogen bonding nor dipolar interactions are accounted for. The Helmholtz energy of a fluid may be written as the sum of different energetic contributions by factorization of partition function. The model developed in this thesis for the pure H{sub 2}O and H{sub 2}S considers three contributions. The first contribution represents the reference Van der Waals fluid which is modelled by the SRK cubic EOS. The second contribution accounts for association through hydrogen bonding and is modelled by a term derived from Cubic Plus Association (CPA) theory. The third contribution corresponds to the dipolar interactions and is modelled by the Mean Spherical Approximation (MSA) theory. The resulting CPAMSA equation has six adjustable parameters, which three represent physical terms whose values are close to their experimental counterpart. This equation results in a better reproduction of the thermodynamic properties of pure water than obtained using the classical CPA equation along the vapour-liquid equilibrium. In addition, extrapolation to higher temperatures and pressure is satisfactory. Similarly, taking into account dipolar interactions together with the SRK cubic equation of state for calculating molar volume of H{sub 2}S as a function of pressure and temperature results in a significant improvement compared to the SRK equation alone. Simple mixing rules between dipolar molecules are proposed to model the H
Equilibrium Analysis in Cake Cutting
DEFF Research Database (Denmark)
Branzei, Simina; Miltersen, Peter Bro
2013-01-01
Cake cutting is a fundamental model in fair division; it represents the problem of fairly allocating a heterogeneous divisible good among agents with different preferences. The central criteria of fairness are proportionality and envy-freeness, and many of the existing protocols are designed...... to guarantee proportional or envy-free allocations, when the participating agents follow the protocol. However, typically, all agents following the protocol is not guaranteed to result in a Nash equilibrium. In this paper, we initiate the study of equilibria of classical cake cutting protocols. We consider one...... of the simplest and most elegant continuous algorithms -- the Dubins-Spanier procedure, which guarantees a proportional allocation of the cake -- and study its equilibria when the agents use simple threshold strategies. We show that given a cake cutting instance with strictly positive value density functions...
Energy Technology Data Exchange (ETDEWEB)
Rosso, Sibele R. [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil); Franceschi, Elton; Borges, Gustavo R.; Corazza, Marcos L.; Oliveira, J. Vladimir [Department of Food Engineering, URI - Campus de Erechim, Av. Sete de Setembro, 1621, Erechim, RS 99700-000 (Brazil); Ferreira, Sandra R.S. [EQA/UFSC, Chemical and Food Engineering Department, Federal University of Santa Catarina, C.P. 476, CEP 88040-900, Florianopolis, SC (Brazil)], E-mail: sandra@enq.ufsc.br
2009-11-15
This work reports phase equilibrium measurements for the ternary systems linoleic (acid + CO{sub 2} + ethanol) and (linolenic acid + CO{sub 2} + ethanol). The fatty acids present in the ternary systems were selected based on composition of banana peel oil extracted by supercritical CO{sub 2} at 20 MPa and 313 K. The motivation of this research relies on the fact that these unsaturated fatty acids are recognized to play an important role in lowering blood pressure and serum cholesterol and because they are present in high concentrations in banana peel extract. Besides that, equilibrium data of these compounds are scarce in literature. The phase equilibrium experiments were performed using a high-pressure variable-volume view cell over the temperature range of (303 to 343) K and pressures up to 19 MPa. For both systems, only vapour-liquid phase transitions were visually recorded for all data measured.
Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow
Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.
2018-02-01
We derive a generalized Grad-Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density.
MHD equilibrium identification on ASDEX-Upgrade
International Nuclear Information System (INIS)
McCarthy, P.J.; Schneider, W.; Lakner, K.; Zehrfeld, H.P.; Buechl, K.; Gernhardt, J.; Gruber, O.; Kallenbach, A.; Lieder, G.; Wunderlich, R.
1992-01-01
A central activity accompanying the ASDEX-Upgrade experiment is the analysis of MHD equilibria. There are two different numerical methods available, both using magnetic measurements which reflect equilibrium states of the plasma. The first method proceeds via a function parameterization (FP) technique, which uses in-vessel magnetic measurements to calculate up to 66 equilibrium parameters. The second method applies an interpretative equilibrium code (DIVA) for a best fit to a different set of magnetic measurements. Cross-checks with the measured particle influxes from the inner heat shield and the divertor region and with visible camera images of the scrape-off layer are made. (author) 3 refs., 3 figs
The equilibrium hydrogen pressure-temperature diagram for the liquid sodium-hydrogen-oxygen system
International Nuclear Information System (INIS)
Knights, C.F.; Whittingham, A.C.
1982-01-01
The underlying equilibria in the sodium-hydrogen-oxygen system are presented in the form of a completmentary hydrogen equilibrium pressure-temperature diagram, constructed by using published data and supplemented by experimental measurements of hydrogen equilibrium pressures over condensed phases in the system. Possible applications of the equilibrium pressure-temperature phase diagram limitations regarding its use are outlined
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
Energy Technology Data Exchange (ETDEWEB)
Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Bhattacharjee, A.; Lazerson, S. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
2015-09-15
We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at the resonant surface.
Phase equilibria basic principles, applications, experimental techniques
Reisman, Arnold
2013-01-01
Phase Equilibria: Basic Principles, Applications, Experimental Techniques presents an analytical treatment in the study of the theories and principles of phase equilibria. The book is organized to afford a deep and thorough understanding of such subjects as the method of species model systems; condensed phase-vapor phase equilibria and vapor transport reactions; zone refining techniques; and nonstoichiometry. Physicists, physical chemists, engineers, and materials scientists will find the book a good reference material.
Unifying dynamical and structural stability of equilibria
Arnoldi, Jean-François; Haegeman, Bart
2016-09-01
We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
Hermite Polynomials and the Inverse Problem for Collisionless Equilibria
Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.
2017-12-01
It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82
Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria
International Nuclear Information System (INIS)
Ling, K.; Abraham-Shrauner, B.
1981-01-01
The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
Sunspot Equilibria in a Production Economy: Do Rational Animal Spirits Cause Overproduction?
Kajii, Atsushi
2008-01-01
We study a standard two period economy with one nominal bond and one firm. The input of the firm is done in the first period and financed with the nominal bond, and its profits are distributed to the shareholders in the second period. We show that a sunspot equilibrium exists around each efficient equilibrium. The interest rate is lower than optimal and there is over production in sunspot equilibria, under some conditions. But a sunspot equilibrium does not exist if the profit share can be tr...
Non-existence of Normal Tokamak Equilibria with Negative Central Current
International Nuclear Information System (INIS)
Hammett, G.W.; Jardin, S.C.; Stratton, B.C.
2003-01-01
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current-drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated
Directory of Open Access Journals (Sweden)
S.M. Moawad
Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices
Stability of relative equilibria of three vortices
DEFF Research Database (Denmark)
Aref, Hassan
2009-01-01
Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably mor...
The feasibility of parameterizing four-state equilibria using relaxation dispersion measurements
International Nuclear Information System (INIS)
Li Pilong; Martins, Ilídio R. S.; Rosen, Michael K.
2011-01-01
Coupled equilibria play important roles in controlling information flow in biochemical systems, including allosteric molecules and multidomain proteins. In the simplest case, two equilibria are coupled to produce four interconverting states. In this study, we assessed the feasibility of determining the degree of coupling between two equilibria in a four-state system via relaxation dispersion measurements. A major bottleneck in this effort is the lack of efficient approaches to data analysis. To this end, we designed a strategy to efficiently evaluate the smoothness of the target function surface (TFS). Using this approach, we found that the TFS is very rough when fitting benchmark CPMG data to all adjustable variables of the four-state equilibria. After constraining a portion of the adjustable variables, which can often be achieved through independent biochemical manipulation of the system, the smoothness of TFS improves dramatically, although it is still insufficient to pinpoint the solution. The four-state equilibria can be finally solved with further incorporation of independent chemical shift information that is readily available. We also used Monte Carlo simulations to evaluate how well each adjustable parameter can be determined in a large kinetic and thermodynamic parameter space and how much improvement can be achieved in defining the parameters through additional measurements. The results show that in favorable conditions the combination of relaxation dispersion and biochemical manipulation allow the four-state equilibrium to be parameterized, and thus coupling strength between two processes to be determined.
Structural Stability of Tokamak Equilibrium: Transport Barriers
Energy Technology Data Exchange (ETDEWEB)
Solano, E. R.
2001-07-01
A generalised theory of structural stability of differential equations is introduced and applied to the Grad-Shafranov equation. It is discussed how the formation and loss of transport barrier could be associated with the appearance/disappearance of equilibria. The equilibrium conjecture is presented: transport barriers are associated with locally diamagnetic regions in the plasma, and affected by the paramagnetism of the bootstrap current. (Author) 18 refs.
Reinaud, J. N.; Sokolovskiy, M. A.; Carton, X.
2017-03-01
We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate the nonlinear evolution of a few selected cases of tripoles.
3D equilibrium codes for mirror machines
International Nuclear Information System (INIS)
Kaiser, T.B.
1983-01-01
The codes developed for cumputing three-dimensional guiding center equilibria for quadrupole tandem mirrors are discussed. TEBASCO (Tandem equilibrium and ballooning stability code) is a code developed at LLNL that uses a further expansion of the paraxial equilibrium equation in powers of β (plasma pressure/magnetic pressure). It has been used to guide the design of the TMX-U and MFTF-B experiments at Livermore. Its principal weakness is its perturbative nature, which renders its validity for high-β calculation open to question. In order to compute high-β equilibria, the reduced MHD technique that has been proven useful for determining toroidal equilibria was adapted to the tandem mirror geometry. In this approach, the paraxial expansion of the MHD equations yields a set of coupled nonlinear equations of motion valid for arbitrary β, that are solved as an initial-value problem. Two particular formulations have been implemented in computer codes developed at NYU/Kyoto U and LLNL. They differ primarily in the type of grid, the location of the lateral boundary and the damping techniques employed, and in the method of calculating pressure-balance equilibrium. Discussions on these codes are presented in this paper. (Kato, T.)
Equilibrium: two-dimensional configurations
International Nuclear Information System (INIS)
Anon.
1987-01-01
In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7
Evaluating measurement uncertainty in fluid phase equilibrium calculations
van der Veen, Adriaan M. H.
2018-04-01
The evaluation of measurement uncertainty in accordance with the ‘Guide to the expression of uncertainty in measurement’ (GUM) has not yet become widespread in physical chemistry. With only the law of the propagation of uncertainty from the GUM, many of these uncertainty evaluations would be cumbersome, as models are often non-linear and require iterative calculations. The methods from GUM supplements 1 and 2 enable the propagation of uncertainties under most circumstances. Experimental data in physical chemistry are used, for example, to derive reference property data and support trade—all applications where measurement uncertainty plays an important role. This paper aims to outline how the methods for evaluating and propagating uncertainty can be applied to some specific cases with a wide impact: deriving reference data from vapour pressure data, a flash calculation, and the use of an equation-of-state to predict the properties of both phases in a vapour-liquid equilibrium. The three uncertainty evaluations demonstrate that the methods of GUM and its supplements are a versatile toolbox that enable us to evaluate the measurement uncertainty of physical chemical measurements, including the derivation of reference data, such as the equilibrium thermodynamical properties of fluids.
Multiple Equilibria in Noisy Rational Expectations Economies
DEFF Research Database (Denmark)
Pálvölgyi, Dömötör; Venter, Gyuri
with a continuous price function. However, we also construct a tractable class of equilibria with discontinuous prices that have very different economic implications, including (i) jumps and crashes, (ii) significant revisions in uninformed belief due to small changes in the market price, (iii) “upward......-sloping” demand curves, (iv) higher prices leading to future returns that are higher in expectation (price drift) and (v) more positively skewed. Discontinuous equilibria can be arbitrarily close to being fully-revealing. Finally, discontinuous equilibria with the same construction also exist in Hellwig (1980)....
Thermodynamic calculations in the system CH4-H2O and methane hydrate phase equilibria
Circone, S.; Kirby, S.H.; Stern, L.A.
2006-01-01
Using the Gibbs function of reaction, equilibrium pressure, temperature conditions for the formation of methane clathrate hydrate have been calculated from the thermodynamic properties of phases in the system CH4-H 2O. The thermodynamic model accurately reproduces the published phase-equilibria data to within ??2 K of the observed equilibrium boundaries in the range 0.08-117 MPa and 190-307 K. The model also provides an estimate of the third-law entropy of methane hydrate at 273.15 K, 0.1 MPa of 56.2 J mol-1 K-1 for 1/n CH4??H 2O, where n is the hydrate number. Agreement between the calculated and published phase-equilibria data is optimized when the hydrate composition is fixed and independent of the pressure and temperature for the conditions modeled. ?? 2006 American Chemical Society.
Numerical equilibrium analysis for structured consumer resource models
de Roos, A.M.; Diekmann, O.; Getto, P.; Kirkilionis, M.A.
2010-01-01
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured re- source. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries
Numerical equilibrium analysis for structured consumer resource models
de Roos, A.M.; Diekmann, O.; Getto, P.; Kirkilionis, M.A.
2010-01-01
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries
International Nuclear Information System (INIS)
Villata, M.; Ferrari, A.
1994-01-01
In the framework of the analytical study of magnetohydrodynamic (MHD) equilibria with flow and nonuniform density, a general family of well-behaved exact solutions of the generalized Grad--Shafranov equation and of the whole set of time-independent MHD equations completed by the nonbarotropic ideal gas equation of state is obtained, both in helical and axial symmetry. The helical equilibrium solutions are suggested to be relevant to describe the helical morphology of some astrophysical jets
Learned helplessness, discouraged workers, and multiple unemployment equilibria in a search model
Bjørnstad, Roger
2001-01-01
Abstract: Unemployment varies strongly between countries with comparable economic structure. Some economists have tried to explain these differences with institutional differences in the labour market. Instead, this paper focuses on a model with multiple equilibria so that the same socioeconomic structure can give rise to different levels of unemployment. Unemployed workers' search efficiency are modelled within an equilibrium search model and lay behind these results. In the model learned...
Donnet, Marcel; Bowen, Paul; Lemaître, Jacques
2009-01-01
Thermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann’s approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thu...
Axisymmetric MHD equilibrium solver with bicubic Hermite elements
International Nuclear Information System (INIS)
Luetjens, H.; Bondeson, A.; Roy, A.
1990-05-01
A numerical code solving axisymmetric magnetohydrodynamic equilibria with rectangular bicubic Hermite elements has been developed. Two test cases are used for checking the convergence rate of the solution. The mapping of the equilibrium quantities into flux coordinates for magnetohydrodynamic stability calculation is performed by a method which preserves the convergence properties of the cubic Hermite elements. Convergence studies show the behaviour of the stability results when the equilibrium mesh is varied. (author) 13 refs., 3 tabs
Three-dimensional stellarator equilibrium as an ohmic steady state
International Nuclear Information System (INIS)
Park, W.; Monticello, D.A.; Strauss, H.; Manickam, J.
1985-07-01
A stable three-dimensional stellarator equilibrium can be obtained numerically by a time-dependent relaxation method using small values of dissipation. The final state is an ohmic steady state which approaches an ohmic equilibrium in the limit of small dissipation coefficients. We describe a method to speed up the relaxation process and a method to implement the B vector . del p = 0 condition. These methods are applied to obtain three-dimensional heliac equilibria using the reduced heliac equations
Neoclassical MHD equilibria with ohmic current
International Nuclear Information System (INIS)
Tokuda, Shinji; Takeda, Tatsuoki; Okamoto, Masao.
1989-01-01
MHD equilibria of tokamak plasmas with neoclassical current effects (neoclassical conductivity and bootstrap current) were calculated self-consistently. Neoclassical effects on JFT-2M tokamak plasmas, sustained by ohmic currents, were studied. Bootstrap currents flow little for L-mode type equilibria because of low attainable values of poloidal beta, β J . H-mode type equilibria give bootstrap currents of 30% ohmic currents for β J attained by JFT-2M and 100% for β J ≥ 1.5, both of which are sufficient to change the current profiles and the resultant MHD equilibria. Neoclassical conductivity which has roughly half value of the classical Spitzer conductivity brings peaked ohmic current profiles to yield low safety factor at the magnetic axis. Neoclassical conductivity reduces the value of effective Z(Z eff ) which is necessary to give the observed one-turn voltage but it needs impurities accumulating at the center when such peaked current profiles are not observed. (author)
Theoretical models of non-Maxwellian equilibria for one-dimensional collisionless plasmas
Allanson, O.; Neukirch, T.; Wilson, F.; Troscheit, S.
2016-12-01
It is ideal to use exact equilibrium solutions of the steady state Vlasov-Maxwell system to intialise collsionless simulations. However, exact equilibrium distribution functions (DFs) for a given macroscopic configuration are typically unknown, and it is common to resort to using `flow-shifted' Maxwellian DFs in their stead. These DFs may be consistent with a macrosopic system with the target number density and current density, but could well have inaccurate higher order moments. We present recent theoretical work on the `inverse problem in Vlasov-Maxwell equilibria', namely calculating an exact solution of the Vlasov equation for a specific given magnetic field. In particular, we focus on one-dimensional geometries in Cartesian (current sheets) coordinates.1. From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials: (O. Allanson, T. Neukirch, S. Troscheit and F. Wilson, Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )2. An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta: (O. Allanson, T. Neukirch, F. Wilson and S. Troscheit, Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])3. Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field (O. Allanson, F. Wilson and T. Neukirch, (2016)) (accepted, Physics of Plasmas)
High temperature interdiffusion and phase equilibria in U-Mo
International Nuclear Information System (INIS)
Lundberg, L.B.
1988-01-01
Experimental data for interdiffusion and phase equilibria in the U-Mo system have been obtained over the temperature range 1400 to 1525 K as a fallout from compatibility experiments in which UO 2 was decomposed by lithium in closed molybdenum capsules. Composition-position, x-ray diffraction and microstructural data from the interdiffusion zones indicate that the intermediate phase U 2 Mo is found in this temperature range, contrary to the currently accepted equilibrium U-Mo phase diagram. The U-Mo interdiffusion data are in good agreement with published values. Inclusion of the U 2 Mo phase in a theoretical correlation of interdiffusion and phase equilibria data using Darken's equation indicate that high temperature interdiffusion of uranium and molybdenum follows the usual thermodynamic rules. Significant changes in the value of the thermodynamic based Darken factor near the U 2 Mo phase boundary on the high uranium side are indicated from both the new and published interdiffusion data. 9 refs., 10 figs., 3 tabs
Phase equilibria in the niobium-vanadium-hydrogen system
Energy Technology Data Exchange (ETDEWEB)
Bethin, J. (Grumman Aerospace Corp., Bethpage, NY (USA)); Welch, D.O. (Brookhaven National Lab., Upton, NY (USA)); Pick, M.A. (Commission of the European Communities, Abingdon (UK). JET Joint Undertaking)
1990-01-01
The effect of vanadium additions to niobium on the metal-hydrogen phase equilibria has been studied. Measurements of the equilibrium H{sub 2}(D{sub 2}) pressure-composition-temperature isotherms for Nb{sub 1-x}V{sub x} alloys with 0{le}x<0.2 were used to determine the depression of the {alpha} - {alpha}' critical temperature with increasing vanadium concentration. A simple lattice-fluid model guided reduction of the data. Changes in the triple point temperature as well as the shift of the {zeta} {yields} {epsilon} phase transition were determined by differential scanning calorimetry measurements. A rapid overall depression was found, of the order of 7 K (at.% substituted V){sup -1}, for the metal-hydrogen (deuterium) phase boundary structure when compared with the Nb-H system in the hydrogen concentration range of interest. The results explain the enhanced terminal solubility of hydrogen in this system found previously by other authors. The changes in the phase equilibria are discussed in terms of the effect of hydrogen trapping and compared with the results of a cluster-variation calculation for random-field systems of previous authors, taking into account a distribution of H-site energies due to alloying. (author).
Inner London Education Authority (England).
This unit on equilibrium is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit, which consists of two levels, focuses on the application of equilibrium principles to equilibria involving weak acids and bases, including buffer solutions and indicators. Level one uses Le Chatelier's…
Ion-molecular equilibria and activity determination in the RbF-ZrF4 system
International Nuclear Information System (INIS)
Skokan, E.V.; Nikitin, M.I.; Sorokin, I.D.; Korenev, Yu.M.; Sidorov, L.N.
1983-01-01
Activity of zirconium tetrofluoride in 100-33.3 mol % ZrF 4 concentration range was determined during isothermal evaporation of samples of different initial composition of RbF-ZrF 4 system, using ion-molecular equilibrium method. It became possible, using the exchange ion-molecular reactions to determine ZrF 4 activity approximately 10 -10 in the region of state diagram of RbF-ZrF 4 system, adjoining to rubidium fluoride. The comparative analysis of results, obtained by the methods of isothermal evaporation, ion-molecular equilibria is given; the advantages and restrictions of ion-molecular equilibrium method are presented
A fast, user-friendly code for calculating magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Haney, S.W.; Freidberg, J.P.; Solomon, C.J.
1995-01-01
Using variational techniques, we have developed a fast, user-friendly code for computing approximate, but highly accurate fixed boundary magnetohydrodynamic equilibria for tokamak plasmas. The variational procedure simplifies the problem---a two-dimensional nonlinear partial differential equation---to a set of nonlinear algebraic equations. The reduced problem can be readily solved on workstations or personal computers. This allows us to exploit sophisticated graphical user interfaces that make supplying calculation data and viewing results easy. This ease-of-use, along with the semianalytic nature of our calculation, allows researchers to routinely incorporate equilibrium information into their work. It also provides a tool for educators teaching fusion theory. We describe the variational formulation, the speed and accuracy of the computer implementation, and the design and operation of a user-friendly graphical interface
Couple specialization in multiple equilibria
Esping-Andersen, G.; Boertien, D.; Bonke, J.; Gracia, P.
2013-01-01
We address the issue of men’s lagged adaptation to the ongoing revolution of women’s roles. This article proposes a multiple equilibrium approach and shows how modes of couple specialization cluster around qualitatively distinct logics. We identify a traditional, egalitarian, and ‘unstable’
Equilibria in social belief removal
CSIR Research Space (South Africa)
Booth, R
2008-09-01
Full Text Available In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a...
Numerical computation of MHD equilibria
International Nuclear Information System (INIS)
Atanasiu, C.V.
1982-10-01
A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)
Route analysis for MHD equilibria
International Nuclear Information System (INIS)
Kikuchi, Fumio; Aizawa, Tatsuhiko
1982-01-01
In Tokamak facilities which are promising in nuclear fusion reactor development, the plasma in the core is often described by MHD approximation. Specifically, since an axisymmetric torus is approximately assumed as the first wall (shell) shape in actual Tokamak facilities, the Grad-Shafranov equation to be satisfied by an axisymmetric equilibrium solution for ideal MHD fluid must be solved, and the characteristics of its solution must be clarified. This paper shows the outline of the numerical calculation which employs both the incremental method taking the particular incremental nodal point values as the control parameters and the interaction method in accordance with Newton method at the same time, the analysis objective being a non-linear eigenvalue problem dealing the boundary of plasma region with surrounding vacuum region as the free boundary. Next, the detailed route analysis of the equilibrium solution is performed, utilizing the above numerical calculation technique, to clarify the effect of shell shape on the behaviour of the equilibrium solution. As the shape of the shell, a rectangular section torus, which have a notch depression at a part of the shell inner boundary, is considered. In the paper, the fundamental MHD equation and its approximate solution by the finite element method, the behaviour of plasma equilibrium solution in a shell having a notch, and the effect of notch shapes on plasma behaviour are described. This analysis verifies the effectiveness of the calculation method. (Wakatsuki, Y.)
Paula Hernandez-Verme; Wen-Yao Wang
2009-01-01
We model a typical Asian-crisis-economy using dynamic general equilibrium tech-niques. Exchange rates obtain from nontrivial fiat-currencies demands. Sudden stops/bank-panics are possible, and key for evaluating the merits of alternative ex-change rate regimes. Strategic complementarities contribute to the severe indetermi-nacy of the continuum of equilibria. The scope for existence and indeterminacy of equilibria and dynamic properties are associated with the underlying policy regime. Bindin...
International Nuclear Information System (INIS)
Horst, J.
1988-11-01
The present work summarizes investigations of the equilibrium of the exchange of protons, copper, zinc, calcium, magnesium and sodium ions on two weak-acid exchange resins in hydrochloric and carbonic acid bearing solutions at 25 0 C. The description of the state of equilibrium between resin and solution is based on the individual chemical equilibria which have to be adjusted simultaneously. The equilibrium in the liquid phase is described by the mass action law and the condition of electroneutrality using activity coefficients calculated according to the theory of Debye and Hueckel. The exchange equilibria are described by means of a surface complex formation model, which was developed by Davis, James and Leckie for activated aluminia and which has been applied to weak-acid resins. The model concept assumes the resin as a plane surface in which the functional groups are distributed uniformly. (orig./RB) [de
Effect of temperature on acid–base equilibria in separation techniques. A review
International Nuclear Information System (INIS)
Gagliardi, Leonardo G.; Tascon, Marcos; Castells, Cecilia B.
2015-01-01
Studies on the theoretical principles of acid–base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid–base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid–liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simplified models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC. - Highlights: • The study of theoretical principles of acid–base equilibrium has been reviewed. • The proton transfer process is often present in the analytical separation practice. • The influence of temperature on secondary chemical equilibria is examined. • The focus is laid on liquid chromatography and capillary electrophoresis. • Temperature can be a useful variable to modify selectivity under predictable basis
A comprehensive theory of the equilibria in a tokamak and a reversed field pinch
International Nuclear Information System (INIS)
Chiyoda, Katsuji
1996-01-01
The equilibrium configuration of a tokamak is analysed by the equilibrium equations derived for analysing a reversed field pinch (RFP). The expressions of the magnetic field and the toroidal shift in the internal plasma region and the external vacuum region are obtained. The expressions in the vacuum region become the Shafranov's expressions, when the plasma-center coordinates is used. Discontinuities of the equilibrium quantities are considered. It is concluded that the equilibrium equations are applicable also to the tokamak plasma and that the difference of the equilibria between the tokamak and the RFP stems from the choices of the pressure and the toroidal current function. A feature of our theory is that any ordering to the safety factor is not imposed. (author)
Fellner, Klemens; Tang, Bao Quoc
2018-06-01
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.
Isotope effects on chemical equilibria
International Nuclear Information System (INIS)
Golding, P.D.
1974-01-01
The thermodynamic equilibrium constants of three deuterated substituted acetic acids are reported. The calculation of secondary isotope effects of the second kind for the three isotopic acid pairs has been accomplished by the appropriate comparison of thermodynamic equilibrium constants, and by the comparison of isotopic slopes. The effect of substituent variation on the isotope effects reported here disqualifies the simple inductive model as a legitimate description of secondary isotope effects of the second kind. The correlation of diminishing isotope effect per deuterium atom with increasing acidity is also invalidated by the present results. The syntheses of 9-thia-9,10-dihydrophenanthrene-9-oxide and thioxanthene-10-oxide are described. These compounds have been partially deuterated at their respective methylene positions. Spectral evidence indicates stereoselectivity of the methylene protons in the exchange reactions of both compounds. (author)
Energy Technology Data Exchange (ETDEWEB)
Anon.
1984-12-15
From 3-6 September the First International Workshop on Local Equilibrium in Strong Interaction Physics took place in Bad-Honnef at the Physics Centre of the German Physical Society. A number of talks covered the experimental and theoretical investigation of the 'hotspots' effect, both in high energy particle physics and in intermediate energy nuclear physics.
African Journals Online (AJOL)
context of antimicrobial therapy in malnutrition. Dialysis has in the past presented technical problems, being complicated and time-consuming. A new dialysis system based on the equilibrium technique has now become available, and it is the principles and practical application of this apparatus (Kontron Diapack; Kontron.
van Damme, E.E.C.
2000-01-01
An outcome in a noncooperative game is said to be self-enforcing, or a strategic equilibrium, if, whenever it is recommended to the players, no player has an incentive to deviate from it.This paper gives an overview of the concepts that have been proposed as formalizations of this requirement and of
Ismail, M.S.
2014-01-01
We introduce a new concept which extends von Neumann and Morgenstern's maximin strategy solution by incorporating `individual rationality' of the players. Maximin equilibrium, extending Nash's value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that
On Equilibria of the Two-fluid Model in Magnetohydrodynamics
International Nuclear Information System (INIS)
Frantzeskakis, Dimitri J.; Stratis, Ioannis G.; Yannacopoulos, Athanasios N.
2004-01-01
We show how the equilibria of the two-fluid model in magnetohydrodynamics can be described by the double curl equation and through the study of this equation we study some properties of these equilibria
International Nuclear Information System (INIS)
Li, Hengde; Han, Yongtao; Huang, Cheng; Yang, Chufen
2015-01-01
Graphical abstract: (Liquid + liquid) equilibrium data for systems composed of β-citronellol and aqueous 1-propanol or acetone are presented. Distribution ratios of 1-propanol and acetone in the mixtures are examined. The effect of the temperature on the ternary (liquid + liquid) equilibria is evaluated and discussed. - Highlights: • Ternary (liquid + liquid) equilibria containing β-citronellol are presented. • Distribution ratios of 1-propanol and acetone in the mixtures are examined. • The effect on the temperature of the systems is evaluated and discussed. - Abstract: On this paper, experimental (liquid + liquid) equilibrium (LLE) results are presented for systems composed of β-citronellol and aqueous 1-propanol or acetone. To evaluate the phase separation properties of β-citronellol in aqueous mixtures, LLE values for the ternary systems (water + 1-propanol + β-citronellol) and (water + acetone + β-citronellol) were determined with a tie-line method at T = (283.15, 298.15, and 313.15 ± 0.02) K and atmospheric pressure. The reliability of the experimental tie-lines was verified by the Hand and Bachman equations. Ternary phase diagrams, distribution ratios of 1-propanol and acetone in the mixtures are shown. The effect of the temperature on the ternary (liquid + liquid) equilibria was examined and discussed. The experimental LLE values were satisfactorily correlated by extended UNIQUAC and modified UNIQUAC models
QUIL: a chemical equilibrium code
International Nuclear Information System (INIS)
Lunsford, J.L.
1977-02-01
A chemical equilibrium code QUIL is described, along with two support codes FENG and SURF. QUIL is designed to allow calculations on a wide range of chemical environments, which may include surface phases. QUIL was written specifically to calculate distributions associated with complex equilibria involving fission products in the primary coolant loop of the high-temperature gas-cooled reactor. QUIL depends upon an energy-data library called ELIB. This library is maintained by FENG and SURF. FENG enters into the library all reactions having standard free energies of reaction that are independent of concentration. SURF enters all surface reactions into ELIB. All three codes are interactive codes written to be used from a remote terminal, with paging control provided. Plotted output is also available
Answer Sets in a Fuzzy Equilibrium Logic
Schockaert, Steven; Janssen, Jeroen; Vermeir, Dirk; de Cock, Martine
Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general “classical” approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.
Existence of pareto equilibria for multiobjective games without compactness
Shiraishi, Yuya; Kuroiwa, Daishi
2013-01-01
In this paper, we investigate the existence of Pareto and weak Pareto equilibria for multiobjective games without compactness. By employing an existence theorem of Pareto equilibria due to Yu and Yuan([10]), several existence theorems of Pareto and weak Pareto equilibria for the multiobjective games are established in a similar way to Flores-B´azan.
Coexistence of equilibria in a New Keynesian model with heterogeneous beliefs
International Nuclear Information System (INIS)
Agliari, Anna; Pecora, Nicolò; Spelta, Alessandro
2015-01-01
The recent macroeconomic literature has been stressing the importance of considering heterogeneous expectations while addressing monetary policy. In this paper we consider a standard New Keynesian model, described by a two-dimensional nonlinear map, to analyze the bifurcation structure when agents have heterogeneous expectations and update their beliefs based on past performance. Depending on the degree of reactivity of the monetary policy to inflation and output deviations from the target equilibrium, different kind of dynamics may occur. We find that multiple equilibria and complicated dynamics, associated to codimension-2 bifurcations, may arise even if the monetary policy is set to respond more than point for point to inflation, as the Taylor principle prescribes. We show that if the monetary policy accommodates for a sufficient degree of output stabilization, complicated dynamics can be avoided and the number of coexisting equilibria reduces.
Schur, W. W.
2004-01-01
Excess in skin material of a pneumatic envelope beyond what is required for minimum enclosure of a gas bubble is a necessary but by no means sufficient condition for the existence of multiple equilibrium configurations for that pneumatic envelope. The very design of structurally efficient super-pressure balloons of the pumpkin shape type requires such excess. Undesired stable equilibria in pumpkin shape balloons have been observed on experimental pumpkin shape balloons. These configurations contain regions with stress levels far higher than those predicted for the cyclically symmetric design configuration under maximum pressurization. Successful designs of pumpkin shape super-pressure balloons do not allow such undesired stable equilibria under full pressurization. This work documents efforts made so far and describes efforts still underway by the National Aeronautics and Space Administration's Balloon Program Office to arrive on guidance on the design of pumpkin shape super-pressure balloons that guarantee full and proper deployment.
Reduction of Islands in Full-pressure Stellarator Equilibria
International Nuclear Information System (INIS)
Hudson, S.R.; Monticello, D.A.; Reiman, A.H.
2001-01-01
The control of magnetic islands is a crucial issue in designing Stellarators. Islands are associated with resonant radial magnetic fields at rational rotational-transform surfaces and can lead to chaos and poor plasma confinement. In this article, we show that variations in the resonant fields of a full-pressure stellarator equilibrium can be related to variations in the boundary via a coupling matrix, and inversion of this matrix determines a boundary modification for which the island content is significantly reduced. The numerical procedure is described and the results of island optimization are presented. Equilibria with islands are computed using the Princeton Iterative Equilibrium Solver, and resonant radial fields are calculated via construction of quadratic-flux-minimizing surfaces. A design candidate for the National Compact Stellarator Experiment [Phys. Plasmas 8, 2001], which has a large island, is used to illustrate the technique. Small variations in the boundary shape are used to reduce island size and to reverse the phase of a major island chain
Validation of equilibrium tools on the COMPASS tokamak
Energy Technology Data Exchange (ETDEWEB)
Urban, J., E-mail: urban@ipp.cas.cz [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Appel, L.C. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Artaud, J.F. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Faugeras, B. [Laboratoire J.A. Dieudonné, UMR 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02 (France); Havlicek, J. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic); Komm, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Lupelli, I. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Peterka, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic)
2015-10-15
Highlights: • Three equilibrium codes—EFIT++, FREEBIE and VacTH—have been successfully set up and validated on COMPASS. • FREEBIE can predictively calculate the equilibrium and corresponding poloidal field coil currents. • EFIT++ can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. • VacTH is a promising tool for real time plasma shape reconstruction. • Optimized parameters are estimated for EFIT++ and VacTH by a statistical analysis. - Abstract: Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code (Appel et al., 2006), the free-boundary equilibrium code FREEBIE (Artaud and Kim, 2012), and a rapid plasma boundary reconstruction code VacTH (Faugeras et al., 2014). We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated.
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
MHD stability of vertically asymmetric tokamak equilibria
International Nuclear Information System (INIS)
Dalhed, H.E.; Grimm, R.C.; Johnson, J.L.
1981-03-01
The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in β becomes important for reactor operation
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
1Quantitative Methods and Information Systems Area, Indian Institute ... The original proof of existence of Nash equilibria [13] uses fairly ...... The fiber over a regular point a of the disk Di consists of three inverse images (labeled. A1,A2,A3 in ...
Equilibrator: Modeling Chemical Equilibria with Excel
Vander Griend, Douglas A.
2011-01-01
Equilibrator is a Microsoft Excel program for learning about chemical equilibria through modeling, similar in function to EQS4WIN, which is no longer supported and does not work well with newer Windows operating systems. Similar to EQS4WIN, Equilibrator allows the user to define a system with temperature, initial moles, and then either total…
Computation of tokamak equilibria with steady flow
International Nuclear Information System (INIS)
Kerner, W.; Tokuda, Shinji
1987-08-01
The equations for ideal MHD equilibria with stationary flow are reexamined and addressed as numerically applied to tokamak configurations with a free plasma boundary. Both the isothermal (purely toroidal flow) and the poloidal flow cases are treated. Experiment-relevant states with steady flow (so far only in the toroidal direction) are computed by the modified SELENE40 code. (author)
On the stability of dissipative MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-04-01
The global stability of stationary equilibria of dissipative MHD is studied uisng the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian system with the full dissipative operators are given. The case of the two-fluid isentropic flow is discussed. (orig.)
Intermediates and Generic Convergence to Equilibria
DEFF Research Database (Denmark)
Marcondes de Freitas, Michael; Wiuf, Carsten; Feliu, Elisenda
2017-01-01
Known graphical conditions for the generic and global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions...
On the stochastic stability of MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-07-01
The stochastic stability in the large of stationary equilibria of ideal and dissipative magnetohydrodynamics under the influence of stationary random fluctuations is studied using the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian systems are given. The destabilizing effect of stochastic fluctuations is demonstrated. (orig.)
Kuiroukidis, Ap.; Throumoulopoulos, G. N.
2015-08-01
We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).
Unique supply function equilibrium with capacity constraints
International Nuclear Information System (INIS)
Holmberg, Paer
2008-01-01
Consider a market where producers submit supply functions to a procurement auction with uncertain demand, e.g. an electricity auction. In the Supply Function Equilibrium (SFE), every firm commits to the supply function that maximises expected profit in the one-shot game given the supply functions of competitors. A basic weakness of the SFE is the presence of multiple equilibria. This paper shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a price cap, and (iv) capacity constraints that bind with a positive probability, there exists a unique, symmetric SFE. (author)
Mirzahosseini, Arash; Somlyay, Máté; Noszál, Béla
2015-08-13
Microscopic redox equilibrium constants, a new species-specific type of physicochemical parameters, were introduced and determined to quantify thiol-disulfide equilibria of biological significance. The thiol-disulfide redox equilibria of glutathione with cysteamine, cysteine, and homocysteine were approached from both sides, and the equilibrium mixtures were analyzed by quantitative NMR methods to characterize the highly composite, co-dependent acid-base and redox equilibria. The directly obtained, pH-dependent, conditional constants were then decomposed by a new evaluation method, resulting in pH-independent, microscopic redox equilibrium constants for the first time. The 80 different, microscopic redox equilibrium constant values show close correlation with the respective thiolate basicities and provide sound means for the development of potent agents against oxidative stress.
Luca Anderlini; Daniele Terlizzese
2009-01-01
We build a simple model of trust as an equilibrium phenomenon, departing from standard "selfish" preferences in a minimal way. Agents who are on the receiving end of an other to transact can choose whether to cheat and take away the entire surplus, taking into account a "cost of cheating." The latter has an idiosyncratic component (an agent's type), and a socially determined one. The smaller the mass of agents who cheat, the larger the cost of cheating suffered by those who cheat. Depending o...
Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games
Directory of Open Access Journals (Sweden)
Kimmo Berg
2017-11-01
Full Text Available This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring. We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called self-supporting sets, since the set itself provides the continuation payoffs that are required to support the equilibrium strategies. Moreover, the corresponding strategies are simple as the players face the same augmented game on each round but they play different mixed actions after each realized pure-action profile. We find that certain payoffs can be obtained in equilibrium with much lower discount factor values compared to pure strategies. The theory and the concepts are illustrated in 2 × 2 games.
Equilibrium and dynamics of uniform density ellipsoidal non-neutral plasmas
International Nuclear Information System (INIS)
Dubin, D.H.E.
1993-01-01
When a single-species plasma is confined in a harmonic Penning trap at cryogenic temperature, the thermal equilibrium is approximately a uniform density spheroid (ellipsoid of revolution). Normal modes corresponding to quadrupole excitations of this plasma have recently been measured. In this paper, nonlinear equations of motion are derived for these quadrupole oscillations. For large amplitudes, the oscillations deform a spheroidal plasma into a triaxial ellipsoid with time-dependent shape and orientation. The integrals of the motion are found and the cylindrically symmetric finite-amplitude oscillations of a spheroid are studied. An analysis of all possible ellipsoidal equilibria is also carried out. New equilibria are discovered which correspond to finite-amplitude versions of the noncylindrically symmetric linear quadrupole oscillations. The equilibria are shown to fall into two classes in which the ellipsoids are either tilted or aligned with respect to the magnetic field. Some of these equilibria have densities well above the Brillouin limit
A toroidal plasma MHD equilibrium code 'EQUCIR version 1'
International Nuclear Information System (INIS)
Ninomiya, Hiromasa; Shinya, Kichiro; Kameari, Akihisa.
1980-10-01
A new free-boundary toroidal MHD equilibrium code ''EQUCIR version 1'' has been developed. The central problems approached by this code is as follows: 1) The magnetic flux distribution of a plasma at equilibrium is determined in the given external field. 2) A set of circuit equations between the plasma and the external conductors are constructed. These circuit equations and the Grad-Shafranov equation are solved self-consistently and the time evolutions of plasma equilibria and currents in external conductors are determined at the same time. 3) The currents in the external conductors are determined so that the plasma cross-section and plasma parameters are to be maintained with desired ones. It is shown that this code is very useful for study of the tokamak plasma equilibria, for design of the poloidal coil system and for investigation of experimental results. (author)
Behavior of magnetic islands in 3D MHD equilibria of helical devices
International Nuclear Information System (INIS)
Hayashi, T.; Sato, T.; Nakajima, N.
1994-09-01
Magnetic island formation in three-dimensional finite-β equilibria in the H-1 Heliac is studied by using the HINT code. It is found that the size of a dangerous island should increase with β but that a destruction of the equilibrium at low β is avoided because the rotational transform evolves to exclude the rational surface concerned. At higher β there is evidence of near-resonant flux surface deformations which may lead to an equilibrium limit. A reconnected equilibrium at still higher β exhibits a double island structure which is similar to homoclinic phase portraits which have been observed after separatrix reconnection in Hamiltonian systems. Physical mechanism of the island formation in finite-β helical equilibria is investigated to confirm there are cases where the global effect of the Pfirsch-Schlueter currents is important. The earlier theory is extended to elucidate the occurence of the complete self-healing of island when the resistive interchange criterion satisfied. (author)
Modeling of LH current drive in self-consistent elongated tokamak MHD equilibria
International Nuclear Information System (INIS)
Blackfield, D.T.; Devoto, R.S.; Fenstermacher, M.E.; Bonoli, P.T.; Porkolab, M.; Yugo, J.
1989-01-01
Calculations of non-inductive current drive typically have been used with model MHD equilibria which are independently generated from an assumed toroidal current profile or from a fit to an experiment. Such a method can lead to serious errors since the driven current can dramatically alter the equilibrium and changes in the equilibrium B-fields can dramatically alter the current drive. The latter effect is quite pronounced in LH current drive where the ray trajectories are sensitive to the local values of the magnetic shear and the density gradient. In order to overcome these problems, we have modified a LH simulation code to accommodate elongated plasmas with numerically generated equilibria. The new LH module has been added to the ACCOME code which solves for current drive by neutral beams, electric fields, and bootstrap effects in a self-consistent 2-D equilibrium. We briefly describe the model in the next section and then present results of a study of LH current drive in ITER. 2 refs., 6 figs., 2 tabs
Surface currents on the plasma-vacuum interface in MHD equilibria
Hanson, James
2017-10-01
The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the interface. While this surface current may be small in MHD equilibrium, it is readily computed in terms of the magnetic potentials in both the interior and exterior regions, evaluated on the surface. If only the external magnetic potential is known (as in VMEC), then the surface current can be computed from the discontinuity of the tangential field across the interface. Examples of the surface current for VMEC equilibria will be shown for a zero-pressure stellarator equilibrium. Field-line following of the vacuum magnetic field shows magnetic islands within the plasma region.
The design of magnetic diagnostics for reconstructing of NCSX stellarator equilibria
International Nuclear Information System (INIS)
Lazarus, E.A.; Pomphrey, N.
2005-01-01
In previous work we have demonstrated that NCSX (National Compact Stellarator Experiment) will require active control of the helical and poloidal field coils in order to remain on a stable trajectory to high beta while retaining quasi-axisymmetry. We require a set of magnetic diagnostics that will be sensitive to changes in the equilibrium that represent departures from such a trajectory. That is, we will need to control features of the plasma boundary shape to a specification; that specification itself will vary with the current and pressure profiles. We need to determine a satisfactory set of magnetic sensors for this task To address this we have postulated a diagnostic set of 443 sensors that we believe is overly complete. A data base of ∼2500 free-boundary equilibria is created with variation of coil currents, plasma pressure and toroidal current profiles, plasma size, total pressure and total current. The signals expected on this array of diagnostics are calculated using a response function formalism. These are used in a linear regression to predict the magnetic field on a smallest vacuum surface that encompasses all the equilibria in the database. We have extended a standard 'variable selection' method of multivariate statistics to determine a complete ranking of the sensors. The ranking scheme is based on properties of the null space of the matrix of diagnostic signals for all equilibria in the database. Subsets are chosen according to this ranking and we judge adequacy by our ability to reconstruct the equilibrium with STELLOPT. While the ability to reconstruct the equilibrium in free boundary does not yield information on optimal control algorithms, it does show whether a particular set of sensors contains the necessary information to allow control of the plasma. Results will be reported. It is yet to be determined just how much information about the profiles can be known from external measurements. We will present results of a study that addresses this
de Oliveira, Mário J
2017-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This new edit...
Acid-base equilibria inside amine-functionalized mesoporous silica.
Yamaguchi, Akira; Namekawa, Manato; Kamijo, Toshio; Itoh, Tetsuji; Teramae, Norio
2011-04-15
Acid-base equilibria and effective proton concentration inside a silica mesopore modified with a trimethyl ammonium (TMAP) layer were studied by steady-state fluorescence experiments. The mesoporous silica with a dense TMAP layer (1.4 molecules/nm(2)) was prepared by a post grafting of N-trimethoxysilylpropyl-N,N,N-trimethylammonium at surfactant-templated mesoporous silica (diameter of silica framework =3.1 nm). The resulting TMAP-modified mesoporous silica strongly adsorbed of anionic fluorescence indicator dyes (8-hydroxypyrene-1,3,6-trisulfonate (pyranine), 8-aminopyrene-1,3,6-trisulfonate (APTS), 5,10,15,20-tetraphenyl-21H,23H-porphinetetrasulfonic acid disulfuric acid (TPPS), 2-naphthol-3,6-disulfonate (2NT)) and fluorescence excitation spectra of these dyes within TMAP-modified mesoporous silica were measured by varying the solution pH. The fluorescence experiments revealed that the acid-base equilibrium reactions of all pH indicator dyes within the TMAP-modified silica mesopore were quite different from those in bulk water. From the analysis of the acid-base equilibrium of pyranine, the following relationships between solution pH (pH(bulk)) and the effective proton concentration inside the pore (pH(pore)) were obtained: (1) shift of pH(pore) was 1.8 (ΔpH(pore)=1.8) for the pH(bulk) change from 2.1 to 9.1 (ΔpH(bulk)=7.0); (2) pH(pore) was not simply proportional to pH(bulk); (3) the inside of the TMAP-modified silica mesopore was suggested to be in a weak acidic or neutral condition when pH(bulk) was changed from 2.0 to 9.1. Since these relationships between pH(bulk) and pH(pore) could explain the acid-base equilibria of other pH indicator dyes (APTS, TPPS, 2NT), these relationships were inferred to describe the effective proton concentration inside the TMAP-modified silica mesopore. © 2011 American Chemical Society
Goya - an MHD equilibrium code for toroidal plasmas
International Nuclear Information System (INIS)
Scheffel, J.
1984-09-01
A description of the GOYA free-boundary equilibrium code is given. The non-linear Grad-Shafranov equation of ideal MHD is solved in a toroidal geometry for plasmas with purely poloidal magnetic fields. The code is based on a field line-tracing procedure, making storage of a large amount of information on a grid unnecessary. Usage of the code is demonstrated by computations of equi/libria for the EXTRAP-T1 device. (Author)
An Equilibrium Analysis of the Gender Wage Gap
Frederiksen, Elisabeth Hermann
2006-01-01
This paper develops a theory of the gender wage gap. In a general equilibrium model, spouses devide their labor between a formal sector and a home sector. Due to indivisibility effects, productivity of labor in the formal sector is negatively related to labor used in the home; at the same time labor inputs are complementary in home production. We show that initial beliefs about the gender wage gap are self-fulfilling, and a central result is multiplicity of equilibria. Spouses allocate their ...
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions.
Computation of zero. beta. three-dimensional equilibria with magnetic islands
Energy Technology Data Exchange (ETDEWEB)
Reiman, A.H.; Greenside, H.S.
1989-01-01
A Picard iteration scheme has been implemented for the computation of toroidal, fully three-dimensional, zero ..beta.. equilibria with islands and stochastic regions. Representation of the variables in appropriate coordinate systems has been found to be a key to making the scheme work well. In particular, different coordinate systems are used for solving magnetic differential equations and Ampere's law. The current profile is adjusted when islands and stochastic regions appear. An underrelaxation of the current profile modifications is generally needed for stable iteration of the algorithm. Some examples of equilibrium calculations are presented. 16 refs., 6 figs., 1 tab.
Gyrokinetic magnetohydrodynamics and the associated equilibria
Lee, W. W.; Hudson, S. R.; Ma, C. H.
2017-12-01
The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee ["Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective," Phys. Plasmas 23, 070705 (2016)], and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, ϕ, and the vector potential, A , and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when ϕ→0 and A becomes constant in time, which, in turn, gives ∇.(J∥+J⊥)=0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. These gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.
Description of gas hydrates equilibria in sediments using experimental data of soil water potential
Energy Technology Data Exchange (ETDEWEB)
Istomin, V. [NOVATEK, Moscow (Russian Federation); Chuvilin, E. [Moscow State Univ., Moscow (Russian Federation). Dept. of Geology; Makhonina, N.; Kvon, V. [VNIIGAZ, Moscow (Russian Federation); Safonov, S. [Schlumberger Moscow Research, Moscow (Russian Federation)
2008-07-01
Analytical relationships have been developed between hydrate dissociation pressure and vapor pressure above the pore water surface. In addition, experiments have been discussed in numerous publications on the effect of narrow interconnected throats between pores on clathrate dissociation conditions in porous media. This paper presented an approach that improved upon the available thermodynamic methods for calculation of hydrate phase equilibria. The approach took into account the properties of pore water in natural sediments including three-phase equilibrium of gas-pore water-gas hydrate in a similar way as for unfrozen water in geocryology science. The purpose of the paper was to apply and adapt geocryology and soil physics method to the thermodynamic calculation of non-clathrated water content in sediments. It answered the question of how to estimate the non-clathrated water content if pore water potential was known. The paper explained the thermodynamics of water phase in porous media including the thermodynamic properties of supercooled water, the thermodynamic properties of pore water and pore ice in sediments, and the phase equilibria of pore water. The paper also discussed the quantitative techniques that were utilized for determination of unfrozen water content in sediments and its dependence on temperature variation. These included contact-saturation, calorimetric, dielectric, nuclear magnetic resonance, and others. The thermodynamic calculations of pore water phase equilibria were also presented. 30 refs., 5 tabs., 8 figs.
Density-functional study on the equilibria in the ThDP activation.
Delgado, Eduardo J; Alderete, Joel B; Jaña, Gonzalo A
2011-11-01
The equilibria among the various ionization and tautomeric states involved in the activation of ThDP is addressed using high level density functional theory calculations, X3LYP/6-311++G(d,p)//X3LYP(PB)/6-31++G(d,p). This study provides the first theoretically derived thermodynamic data for the internal equilibria in the activation of ThDP. The role of the medium polarity on the geometry and thermodynamics of the diverse equilibria of ThDP is addressed. The media chosen are cyclohexane and water, as paradigms of apolar and polar media. The results suggest that all ionization and tautomeric states are accessible during the catalytic cycle, even in the absence of substrate, being APH(+) the form required to interconvert the AP and IP tautomers; and the generation of the ylide proceeds via the formation of the IP form. Additionally, the calculated ΔG° values allow to calculate all the equilibrium constants, including the pK(C2) for the thiazolium C2 atom whose ionization is believed to initiate the catalytic cycle.
On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem.
Directory of Open Access Journals (Sweden)
Jiawei Li
Full Text Available In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games.
On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem
Li, Jiawei; Kendall, Graham
2015-01-01
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088
International Nuclear Information System (INIS)
Meloun, M.; Havel, J.; Hogfeldt, E.
1988-01-01
Although this book contains a very good review of computation methods applicable to equilibrium systems, most of the book is dedicated to the description and evaluation of computer programs available for doing such calculations. As stated in the preface, the authors (two computniks and a user of graphical and computer methods) have joined forces in order to present the reader with the points of view of both the creator and user of modern computer program tools available for the study of solution equilibria. The successful presentation of such a complicated amalgamation of concepts is greatly aided by the structure of the book, which begins with a brief but thorough discussion of equilibrium concepts in general, followed by an equally brief discussion of experimental methods used to study equilibria with potentiometric, extraction, and spectroscopic methods. These sections would not be sufficient to teach these topics to the beginner but offer an informative presentation of concepts in relation to one another to those already familiar with basic equilibrium concepts. The importance of evaluating and analyzing the suitability of data for further analysis is then presented before an in depth (by a chemist's standards) look at the individual parts that make up a detailed equilibrium analysis program. The next one-third of the book is an examination of specific equilibrium problems and the programs available to study them. These are divided into chapters devoted to potentiometric, extraction, and spectroscopic methods. The format is to discuss a variety of programs, one at a time, including the parts of the program, the types of problems to which it has been applied, and the program's limitations. A number of problems are then presented, which are representative of the type of questions that are normally addressed by research projects in the area
Multiple Equilibria in Noisy Rational Expectations Economies
DEFF Research Database (Denmark)
Palvolgyi, Domotor; Venter, Gyuri
This paper studies equilibrium uniqueness in standard noisy rational expectations economies with asymmetric or differential information a la Grossman and Stiglitz (1980) and Hellwig (1980). We show that the standard linear equilibrium of Grossman and Stiglitz (1980) is the unique equilibrium...
Phase Equilibria of Sn-Co-Cu Ternary System
Chen, Yu-Kai; Hsu, Chia-Ming; Chen, Sinn-Wen; Chen, Chih-Ming; Huang, Yu-Chih
2012-10-01
Sn-Co-Cu ternary alloys are promising lead-free solders, and isothermal sections of Sn-Co-Cu phase equilibria are fundamentally important for the alloys' development and applications. Sn-Co-Cu ternary alloys were prepared and equilibrated at 523 K, 1073 K, and 1273 K (250 °C, 800 °C, and 1000 °C), and the equilibrium phases were experimentally determined. In addition to the terminal solid solutions and binary intermetallic compounds, a new ternary compound, Sn3Co2Cu8, was found. The solubilities of Cu in the α-CoSn3 and CoSn2 phases at 523 K (250 °C) are 4.2 and 1.6 at. pct, respectively, while the Cu solubility in the α-Co3Sn2 phase is as high as 20.0 at. pct. The Cu solubility increases with temperature and is around 30.0 at. pct in the β-Co3Sn2 at 1073 K (800 °C). The Co solubility in the η-Cu6Sn5 phase is also significant and is 15.5 at. pct at 523 K (250 °C).
Convergence in gradient systems with branching of equilibria
International Nuclear Information System (INIS)
Galaktionov, V A; Pohozaev, Stanislav I; Shishkov, A E
2007-01-01
The basic model is a semilinear elliptic equation with coercive C 1 non-linearity: Δψ+f(ψ)=0 in Ω, ψ=0 on ∂Ω, where Ω subset of R N is a bounded smooth domain. The main hypothesis (H R ) about resonance branching is as follows: if a branching of equilibria occurs at a point ψ with k-dimensional kernel of the linearized operator Δ+f'(ψ)I, then the branching subset S k at ψ is a locally smooth k-dimensional manifold. For N=1 the first result on the stabilization to a single equilibrium is due to Zelenyak (1968). It is shown that Zelenyak's approach, which is based on the analysis of Lyapunov functions, can be extended to general gradient systems in Hilbert spaces with smooth resonance branching. The case of asymptotically small non-autonomous perturbations of such systems is also considered. The approach developed here represents an alternative to Hale's stabilization method (1992) and other similar techniques in the theory of gradient systems. Bibliography: 32 titles.
Longitudinal traveling waves bifurcating from Vlasov plasma equilibria
International Nuclear Information System (INIS)
Holloway, J.P.
1989-01-01
The kinetic equations governing longitudinal motion along a straight magnetic field in a multi-species collisionless plasma are investigated. A necessary condition for the existence of small amplitude spatially periodic equilibria and traveling waves near a given spatially uniform background equilibrium is derived, and the wavelengths which such solutions must approach as their amplitude decreases to zero are discussed. A sufficient condition for the existence of these small amplitude waves is also established. This is accomplished by studying the nonlinear ODE for the potential which arises when the distribution functions are represented in a BGK form; the arbitrary functions of energy that describe the BGK representation are tested as an infinite dimensional set of parameters in a bifurcation theory for the ODE. The positivity and zero current condition in the wave frame of the BGK distribution functions are maintained. The undamped small amplitude nonlinear waves so constructed can be made to satisfy the Vlasov dispersion relation exactly, but in general they need only satisfy it approximately. Numerical calculations reveal that even a thermal equilibrium electron-proton plasma with equal ion and electron temperatures will support undamped traveling waves with phase speeds greater than 1.3 times the electron velocity; the dispersion relation for this case exhibits both Langmuir and ion-acoustic branches as long wavelength limits, and shows how these branches are in fact connected by short wavelength waves of intermediate frequency. In apparent contradiction to the linear theory of Landau, these exact solutions of the kinetic equations do not damp; this contradiction is explained by observing that the linear theory is, in general, fundamentally incapable of describing undamped traveling waves
International Nuclear Information System (INIS)
Wan, Li; Li, Hengde; Huang, Cheng; Feng, Yuqing; Chu, Guoqiang; Zheng, Yuying; Tan, Wei; Qin, Yanlin; Sun, Dalei; Fang, Yanxiong
2017-01-01
Highlights: • Ternary LLEs containing linalool and geraniol are presented. • Distribution ratios of 1-propanol in the mixtures are examined. • Influence of the temperature on the LLE is studied. • The LLE data were correlated using the NRTL and UNIQUAC models. - Abstract: Linalool and geraniol are the primary components of rose oil, palmarosa oil, and citronella oil and many other essential oils, and two important compounds used in the flavour and fragrance, cosmetic or pharmaceutical industries. Phase equilibria (LLE, VLE, solubility, etc.) and related thermodynamic properties of a mixture are essential in the processes design and control of mass transfer process. In this work, experimental (liquid + liquid) equilibria data of the systems (water + 1-propanl + linalool) and (water + 1-propanl + geraniol) are presented. The (liquid + liquid) equilibria of both systems were determined with a tie-line method at T = (283.15, 298.15 and 313.15) K under atmospheric pressure. The well-known Hand, Bachman and Othmer–Tobias equations were used to test the reliability of the experimental values. The influence of the temperature on the (liquid + liquid) phase equilibria of the mixtures, the binodal curves and distribution ratios of 1-propanl are shown and discussed. Moreover, the NRTL and UNIQUAC models were applied to fit the data for both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. Furthermore, the ternary systems could be represented using the binary parameters of the thermodynamic model with a function of temperature.
Use of the stellarator expansion to investigate plasma equilibrium in modular stellarators
International Nuclear Information System (INIS)
Anania, G.; Johnson, J.L.; Weimer, K.E.
1982-11-01
A numerical code utilizing a large-aspect ratio, small-helical-distortion expansion is developed and used to investigate the effect of plasma currents on stellarator equilibrium. Application to modular stellarator configurations shows that a large rotational transform, and hence large coil deformation, is needed to achieve high-beta equilibria
On the Open-Loop Nash Equilibrium in LQ-Games
Engwerda, J.C.
1996-01-01
In this paper we consider open-loop Nash equilibria of the linear-quadratic differential game.As well the finite-planning-horizon, the infinite-planning horizon as convergence properties of the finite-planning-horizon equilibrium if the planning horizon is extended to infinity are studied.Particular
Equilibrium and nonequilibrium attractors for a discrete, selection-migration model
James F. Selgrade; James H. Roberds
2003-01-01
This study presents a discrete-time model for the effects of selection and immigration on the demographic and genetic compositions of a population. Under biologically reasonable conditions, it is shown that the model always has an equilibrium. Although equilibria for similar models without migration must have real eigenvalues, for this selection-migration model we...
On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: mnjmhd@am.uva.es
2008-06-16
While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.
Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
International Nuclear Information System (INIS)
Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.
1988-01-01
Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed
Experimental determination of thermodynamic equilibrium in biocatalytic transamination.
Tufvesson, Pär; Jensen, Jacob S; Kroutil, Wolfgang; Woodley, John M
2012-08-01
The equilibrium constant is a critical parameter for making rational design choices in biocatalytic transamination for the synthesis of chiral amines. However, very few reports are available in the scientific literature determining the equilibrium constant (K) for the transamination of ketones. Various methods for determining (or estimating) equilibrium have previously been suggested, both experimental as well as computational (based on group contribution methods). However, none of these were found suitable for determining the equilibrium constant for the transamination of ketones. Therefore, in this communication we suggest a simple experimental methodology which we hope will stimulate more accurate determination of thermodynamic equilibria when reporting the results of transaminase-catalyzed reactions in order to increase understanding of the relationship between substrate and product molecular structure on reaction thermodynamics. Copyright © 2012 Wiley Periodicals, Inc.
Calculation of Multiphase Chemical Equilibrium by the Modified RAND Method
DEFF Research Database (Denmark)
Tsanas, Christos; Stenby, Erling Halfdan; Yan, Wei
2017-01-01
method. The modified RAND extends the classical RAND method from single-phase chemical reaction equilibrium of ideal systems to multiphase chemical equilibrium of nonideal systems. All components in all phases are treated in the same manner and the system Gibbs energy can be used to monitor convergence....... This is the first time that modified RAND was applied to multiphase chemical equilibrium systems. The combined algorithm was tested using nine examples covering vapor–liquid (VLE) and vapor–liquid–liquid equilibria (VLLE) of ideal and nonideal reaction systems. Successive substitution provided good initial......A robust and efficient algorithm for simultaneous chemical and phase equilibrium calculations is proposed. It combines two individual nonstoichiometric solving procedures: a nested-loop method with successive substitution for the first steps and final convergence with the second-order modified RAND...
International Nuclear Information System (INIS)
Barnes, D.C.; Brackbill, J.U.
1977-01-01
A numerical study of the equilibrium and stability properties of the Scyllac experiment at Los Alamos is described. The formulation of the numerical method, which is an extension of the ICED-ALE method to magnetohydrodynamic flow in three dimensions, is given. The properties of the method are discussed, including low computational diffusion, local conservation, and implicit formulation in the time variable. Also discussed are the problems encountered in applying boundary conditions and computing equilibria. The results of numerical computations of equilibria indicate that the helical field amplitudes must be doubled from their design values to produce equilibrium in the Scyllac experiment. This is consistent with other theoretical and experimental results
Ballooning stable high beta tokamak equilibria
International Nuclear Information System (INIS)
Tuda, Takashi; Azumi, Masafumi; Kurita, Gen-ichi; Takizuka, Tomonori; Takeda, Tatsuoki
1981-04-01
The second stable regime of ballooning modes is numerically studied by using the two-dimensional tokamak transport code with the ballooning stability code. Using the simple FCT heating scheme, we find that the plasma can locally enter this second stable regime. And we obtained equilibria with fairly high beta (β -- 23%) stable against ballooning modes in a whole plasma region, by taking into account of finite thermal diffusion due to unstable ballooning modes. These results show that a tokamak fusion reactor can operate in a high beta state, which is economically favourable. (author)
Critical beta for analytical spheromak equilibria
International Nuclear Information System (INIS)
Freire, E.M.; Clemente, R.A.
1985-01-01
The Mercier criterion is applied to two analytical spheromak equilibria, one with a spherical separatrix and the other with a cylindrical one of variable elongation. The maximum beta, defined as the ratio between the plasma pressure and the magnetic pressure averaged over the plasma volume, for which the criterion is satisfied on every magnetic surface, has been obtained. In the spherical model the critical beta is 0.003, while in the cylindrical case it is a function of the elongation of the separatrix with a maximum of 0.083. (author)
Correlated equilibria in homogenous good Bertrand competition
DEFF Research Database (Denmark)
Jann, Ole; Schottmüller, Christoph
2015-01-01
We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogenous goods and identical marginal costs. This provides a theoretical underpinning for the so-called "Bertrand paradox'' as well as its most general f...... formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in the following way: The market price cannot be higher than the second lowest marginal cost in any correlated equilibrium....
Axiomatizations of Pareto Equilibria in Multicriteria Games
Voorneveld, M.; Vermeulen, D.; Borm, P.E.M.
1997-01-01
We focus on axiomatizations of the Pareto equilibrium concept in multicriteria games based on consistency.Axiomatizations of the Nash equilibrium concept by Peleg and Tijs (1996) and Peleg, Potters, and Tijs (1996) have immediate generalizations.The axiomatization of Norde et al.(1996) cannot be
Moulas, E.; Caddick, M. J.; Tisato, N.; Burg, J.-P.
2012-04-01
The investigation of metamorphic phase equilibria, using software packages that perform thermodynamic calculations, involves a series of important assumptions whose validity can often be questioned but are difficult to test. For example, potential influences of deformation on phase relations, and modification of effective reactant composition (X) at successive stages of equilibrium may both introduce significant uncertainty into phase diagram calculations. This is generally difficult to model with currently available techniques, and is typically not well quantified. We present here a method to investigate such phenomena along pre-defined Pressure-Temperature (P-T) paths, calculating local equilibrium via Gibbs energy minimization. An automated strategy to investigate complex changes in the effective equilibration composition has been developed. This demonstrates the consequences of specified X modification and, more importantly, permits automated calculation of X changes that are likely along the requested path if considering several specified processes. Here we describe calculations considering two such processes and show an additional example of a metamorphic texture that is difficult to model with current techniques. Firstly, we explore the assumption that although water saturation and bulk-rock equilibrium are generally considered to be valid assumptions in the calculation of phase equilibria, the saturation of thermodynamic components ignores mechanical effects that the fluid/melt phase can impose on the rock, which in turn can modify the effective equilibrium composition. Secondly, we examine how mass fractionation caused by porphyroblast growth at low temperatures or progressive melt extraction at high temperatures successively modifies X out of the plane of the initial diagram, complicating the process of determining best-fit P-T paths for natural samples. In particular, retrograde processes are poorly modeled without careful consideration of prograde
Inclusion of pressure and flow in the KITES MHD equilibrium code
International Nuclear Information System (INIS)
Raburn, Daniel; Fukuyama, Atsushi
2013-01-01
One of the simplest self-consistent models of a plasma is single-fluid magnetohydrodynamic (MHD) equilibrium with no bulk fluid flow under axisymmetry. However, both fluid flow and non-axisymmetric effects can significantly impact plasma equilibrium and confinement properties: in particular, fluid flow can produce profile pedestals, and non-axisymmetric effects can produce islands and stochastic regions. There exist a number of computational codes which are capable of calculating equilibria with arbitrary flow or with non-axisymmetric effects. Previously, a concept for a code to calculate MHD equilibria with flow in non-axisymmetric systems was presented, called the KITES (Kyoto ITerative Equilibrium Solver) code. Since then, many of the computational modules for the KITES code have been completed, and the work-in-progress KITES code has been used to calculate non-axisymmetric force-free equilibria. Additional computational modules are required to allow the KITES code to calculate equilibria with pressure and flow. Here, the authors report on the approaches used in developing these modules and provide a sample calculation with pressure. (author)
MHD equilibrium of toroidal fusion plasma with stationary flows
International Nuclear Information System (INIS)
Galkowski, A.
1994-01-01
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad's ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs
CFD analysis of laboratory scale phase equilibrium cell operation
Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville
2017-10-01
For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process.: Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.
CFD analysis of laboratory scale phase equilibrium cell operation.
Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville
2017-10-01
For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.
Effect of Equilibrium Flow on Plasma Parameters
International Nuclear Information System (INIS)
Mukhopadhyay, S.; Lahiri, S.; Sakanaka, P.H.; Dasgupta, B.
2003-01-01
The transition to high confinement modes have been identified with the occurrence of strong shear flow near the plasma boundary. Plasma flow has also been associated with various instabilities, heating and other physical processes. As a result, it has become very important to study the effect of such flows on various plasma parameters. In this paper, we present the numerical solution of plasma equilibrium with incompressible toroidal and poloidal flows in several magnetic confinement configurations including tokamaks. The code, which was reported in the last conference, has been used to solve the problem in both circular and D-shaped devices. A parametric study on the generation of shear flow due to radial electric fields has been carried out. Through this study, it has been possible to generate plasma equilibria having sharp pressure gradients which are remarkably close to those reported in various H-mode experiments. The effects of flow on reverse shear equilibria and on the position of the magnetic axis has been studied. Finally, a detailed study has been carried out to understand the effect of flows on important plasma parameters, such as the poloidal flux function, β, energy confinement time
Equilibria model for pH variations and ion adsorption in capacitive deionization electrodes.
Hemmatifar, Ali; Oyarzun, Diego I; Palko, James W; Hawks, Steven A; Stadermann, Michael; Santiago, Juan G
2017-10-01
Ion adsorption and equilibrium between electrolyte and microstructure of porous electrodes are at the heart of capacitive deionization (CDI) research. Surface functional groups are among the factors which fundamentally affect adsorption characteristics of the material and hence CDI system performance in general. Current CDI-based models for surface charge are mainly based on a fixed (constant) charge density, and do not treat acid-base equilibria of electrode microstructure including so-called micropores. We here expand current models by coupling the modified Donnan (mD) model with weak electrolyte acid-base equilibria theory. In our model, surface charge density can vary based on equilibrium constants (pK's) of individual surface groups as well as micropore and electrolyte pH environments. In this initial paper, we consider this equilibrium in the absence of Faradaic reactions. The model shows the preferential adsorption of cations versus anions to surfaces with respectively acidic or basic surface functional groups. We introduce a new parameter we term "chemical charge efficiency" to quantify efficiency of salt removal due to surface functional groups. We validate our model using well controlled titration experiments for an activated carbon cloth (ACC), and quantify initial and final pH of solution after adding the ACC sample. We also leverage inductively coupled plasma mass spectrometry (ICP-MS) and ion chromatography (IC) to quantify the final background concentrations of individual ionic species. Our results show a very good agreement between experiments and model. The model is extendable to a wide variety of porous electrode systems and CDI systems with applied potential. Copyright © 2017 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Hasegawa, Yukihiro; Nakamura, Yukiharu; Shirai, Hiroshi; Hamamatsu, Kiyotaka; Harada, Yoshio; Kikuchi, Mitsuru; Nakata, Yoshihiro
1999-01-01
In order to provide a set of magnetohydrodynamic (MHD) equilibrium database which is indispensable for both the studies on improvement of energy confinement and stabilization of MHD activities in tokamaks, a high speed data-processing system synchronizing with J T-60 discharge sequence was newly developed by utilizing the latest model of hugh speed workstation and by optimizing the parallel processing technique to perform fast calculation of MHD equilibria. This high speed system was found to have a sufficient ability to complete the whole equilibrium calculations during each inter-shot period. Cooperating with the mass data storage subsystem preserving the latest equilibrium database automatically, the animated discharge monitoring subsystem provides valuable information for the J T-60 operator to determine control parameters of the succeeding discharge. This report describes the system performance realized in the J T-60 experiment. (author)
International Nuclear Information System (INIS)
Azis, Abdul; Teramoto, Masaaki; Matsuyama, Hideto.
1995-01-01
Equilibrium and non-equilibrium extraction separations of rare earth metals were carried out in the presence of chelating agent in the aqueous phase. The separation systems of the rare earth metal mixtures used were Y/Dy, Y/Ho, Y/Er and Y/Tm, and the chelating agent and the extractant were diethylenetriaminepentaacetic acid (DTPA) and bis (2,4,4-trimethylpentyl) phosphinic acid (CYANEXR 272), respectively. For Y/Dy and Y/Ho systems, higher selectivities were obtained in equilibrium separation compared with those in non-equilibrium separation. On the other hand, the selectivities in non-equilibrium separation were higher for Y/Er and Y/Tm systems. In the separation condition suitable to each system, the addition of DTPA to the aqueous phase was found to be very effective for obtaining higher selectivities. The distribution ratios of the rare earth metals and the selectivities in the equilibrium separations obtained experimentally were thoroughly analyzed by considering various equilibria such as the extraction equilibrium and the complex formation equilibrium between rare earth metals and DTPA in the aqueous phase. Moreover, the extraction rates and the selectivities in the non-equilibrium separations were also analyzed by the extraction model considering the dissociation reactions of the rare earth metal-DTPA complexes in the aqueous stagnant layer. Based on these analyses, we presented an index which is useful for selecting the optimum operation mode. Using this index, we can predict that the selectivities under equilibrium conditions are higher than those under non-equilibrium conditions for Y/Dy and Y/Ho systems, while for Y/Er and Y/Tm systems, higher selectivities are obtained under non-equilibrium conditions. The experimental results were in agreement with predictions by this index. Further, the selectivities in various systems including other chelating agents and extractants were discussed based on this index. (J.P.N.)
Isotopic equilibria between sulphur solute species at high temperature
International Nuclear Information System (INIS)
Robinson, B.W.
1978-01-01
Sulphur solute species in ore solutions and geothermal discharges include HSO 4 - , SO 4 2- , H 2 S, and HS - , as well as the ion-paired species, NaHS 0 , NaHSO 4 - and Na 2 SO 4 0 . Observed sulphate-sulphide fractionation factors and the rates of attainment of isotopic equilibrium are likely to depend on the nature of the sulphur species actually taking part in these isotopic equilibria. Preliminary experiments in alkaline solution (pH 10.1 at 20 0 C) were carried out in a gold cell. No significant isotope fractionation was observed between the SO 4 2- and HS - in 29 days at 200 0 C, 63days at 300 0 C, or 90 days at 250 0 C. However, similar experiments at 350 0 C in sealed gold capsules at room temperature pH 8.5 showed slow exchange(t( 1 / 2 ) was calculated to be 510 days for the SO 4 2- -HS - exchange reaction using the theoretical fractionation of 20.2 0 / 00 ). The addition of NaCl appeared to have no affect on the exchange. However, pH strongly controls the reaction rate, and exchange probably involves H 2 S and the HSO 4 - ion. Additional preliminary experiments were conducted with a fivefold increase in the sulphur concentration; a decrease in t( 1 / 2 ) to 142 days resulted. Some inter-relationship between sulphur concentration and exchange rate thus exists. The important controlling parameters of isotope exchange (temperature, pH, and ΣS) can be seen to have influenced exchange in natural systems.(auth.)
International Nuclear Information System (INIS)
Li Hengde; Tamura, Kazuhiro
2006-01-01
(Liquid + liquid) equilibria and tie-lines for the ternary (water + ethanol + α-pinene, or β-pinene or limonene) and quaternary (water + ethanol + α-pinene + limonene) mixtures have been measured at T = 298.15 K. The experimental multicomponent (liquid + liquid) equilibrium data have been successfully represented in terms of the modified UNIQUAC model with binary parameters
Ternary equilibria in bismuth--indium--lead alloys
International Nuclear Information System (INIS)
Liao, K.C.; Johnson, D.L.; Nelson, R.C.
1975-01-01
The liquidus surface is characterized by three binary equilibria. One binary extends from the Pb--Bi peritectic to the Pb--In peritectic. The other two extend from In--Bi eutectics, merge at 50 at. percent Bi and 30 at. percent Pb, and end at the Bi--Pb eutectic. Based on analysis of ternary liquidus contours and vertical sections, it is suggested that solidification for high lead and very high indium alloys occurs from two-phase equilibria. Solidification from all other alloys occurs from three-phase equilibria. Four-phase solidification does not occur in this system
On Pure and (approximate) Strong Equilibria of Facility Location Games
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm; Telelis, Orestis A.
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every...... agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stability (PoS) of pure Nash equilibria and the Price of Anarchy of strong equilibria (SPoA), that generalize pure equilibria by being resilient to coalitional deviations. For unweighted agents on metric...
Effect of impurity radiation on tokamak equilibrium
International Nuclear Information System (INIS)
Rebut, P.H.; Green, B.J.
1977-01-01
The energy loss from a tokamak plasma due to the radiation from impurities is of great importance in the overall energy balance. Taking the temperature dependence of this loss for two impurities characteristic of those present in existing tokamak plasmas, the condition for radial power balance is derived. For the impurities considered (oxygen and iron) it is found that the radiation losses are concentrated in a thin outer layer of the plasma and the equilibrium condition places an upper limit on the plasma paraticle number density in this region. This limiting density scales with mean current density in the same manner as is experimentally observed for the peak number density of tokamak plasmas. The stability of such equilibria is also discussed. (author)
Equilibrium and stability in strongly inhomogeneous plasmas
International Nuclear Information System (INIS)
Mynick, H.E.
1978-10-01
The equilibrium of strongly inhomogeneous, collisionless, slab plasmas, is studied using a generalized version of a formalism previously developed, which permits the generation of self-consistent equilibria, for plasmas with arbitrary magnetic shear, and variation of magnetic field strength. A systematic procedure is developed for deriving the form of the guiding-center Hamiltonian K, for finite eta, in an axisymmetric geometry. In the process of obtaining K, an expression for the first adiabatic invariant (the gyroaction) is obtained, which generalizes the usual expression 1/2 mv/sub perpendicular/ 2 /Ω/sub c/ (Ω/sub c/ = eB/mc), to finite eta and magnetic shear. A formalism is developed for the study of the stability of strongly-inhomogeneous, magnetized slab plasmas; it is then applied to the ion-drift-cyclotron instability
Existence of equilibria in articulated bearings
Buscaglia, G.; Ciuperca, I.; Hafidi, I.; Jai, M.
2007-04-01
The existence of equilibrium solutions for a lubricated system consisting of an articulated body sliding over a flat plate is considered. Though this configuration is very common (it corresponds to the popular tilting-pad thrust bearings), the existence problem has only been addressed in extremely simplified cases, such as planar sliders of infinite width. Our results show the existence of at least one equilibrium for a quite general class of (nonplanar) slider shapes. We also extend previous results concerning planar sliders.
Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD
Ferraro, N. M.
2015-11-01
The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. This research was supported by US DOE contracts DE-FG02-95ER54309, DE-FC02-04ER54698 and DE-AC52-07NA27344.
Equilibrium Droplets on Deformable Substrates: Equilibrium Conditions.
Koursari, Nektaria; Ahmed, Gulraiz; Starov, Victor M
2018-05-15
Equilibrium conditions of droplets on deformable substrates are investigated, and it is proven using Jacobi's sufficient condition that the obtained solutions really provide equilibrium profiles of both the droplet and the deformed support. At the equilibrium, the excess free energy of the system should have a minimum value, which means that both necessary and sufficient conditions of the minimum should be fulfilled. Only in this case, the obtained profiles provide the minimum of the excess free energy. The necessary condition of the equilibrium means that the first variation of the excess free energy should vanish, and the second variation should be positive. Unfortunately, the mentioned two conditions are not the proof that the obtained profiles correspond to the minimum of the excess free energy and they could not be. It is necessary to check whether the sufficient condition of the equilibrium (Jacobi's condition) is satisfied. To the best of our knowledge Jacobi's condition has never been verified for any already published equilibrium profiles of both the droplet and the deformable substrate. A simple model of the equilibrium droplet on the deformable substrate is considered, and it is shown that the deduced profiles of the equilibrium droplet and deformable substrate satisfy the Jacobi's condition, that is, really provide the minimum to the excess free energy of the system. To simplify calculations, a simplified linear disjoining/conjoining pressure isotherm is adopted for the calculations. It is shown that both necessary and sufficient conditions for equilibrium are satisfied. For the first time, validity of the Jacobi's condition is verified. The latter proves that the developed model really provides (i) the minimum of the excess free energy of the system droplet/deformable substrate and (ii) equilibrium profiles of both the droplet and the deformable substrate.
Isotope anomalies in oxygen isotope exchange equilibrium systems
International Nuclear Information System (INIS)
Kotaka, M.
1997-01-01
The purpose of the present work is to elucidate the isotope anomalies in oxygen isotope exchange equilibrium systems, according to the calculations of the equilibrium constants for oxygen isotopic exchange reactions, and the calculations of the oxygen isotope separation factors between two phases. The equilibrium constants (K65, K67, K68 and K69) of 16 O- 15 O, 16 O 17 O, 16 O- 18 O, and 16 O- 19 O exchange reactions between diatomic oxides were calculated in a wide temperature range on the basis of quantum statistical mechanics. Many equilibrium constants showed the anomalous mass effects, and then had the crossover temperatures and the mass independent fractionation (MIF) temperatures which held K67 = K65, K67 = K68, or K67 = K69, etc. For example, the equilibrium constants for the reactions between OH and the other diatomic oxides (MO) showed the anomalous mass effects, when M was Li, Na, Mg, K, Fe, Al, Ge, Zr, Pt, etc. The 16 O 15 O, 16 O 17 O, 16 O- 18 O, and 16 O- 19 O oxygen isotope separation factors (S65, S67, S68 and S69) between two phases were calculated, when OH and CO were in the first phase, and SiO was in the second phase. Although the oxygen isotopic exchange equilibria in the two phases had no MIF and crossover temperatures, the separation factors showed the anomalous mass effects and had the temperatures. According to what is called the normal mass effects for the equilibrium constant of isotopic exchange reaction, the value of InK68/InK67 is 1.885. Therefore, the value of InS68/InS67 should be 1.885 too. The value calculated, however, widely changed. It can be concluded from the results obtained in the present work that some oxygen isotopic exchange equilibria cause the anomalous mass effects, the anomalous oxygen isotope separation factors, and then isotope anomalies
A study of electron-positron pair equilibria in models of compact X- and gamma-ray sources
International Nuclear Information System (INIS)
Bjoernsson, G.
1990-01-01
Thermal electron-positron pair equilibria in two temperature models of compact x ray and gamma ray sources are studied. The pairs are assumed to be heated by Coulomb interaction with the much hotter protons and cooled by bremsstrahlung emission, Compton scattering, and annihilation. Two parameters, the proton optical depth and the compactness, characterize each equilibrium state. It is shown that a careful account of the energy balance is very important when the stability properties of the pair equilibria in a spherical plasma cloud are determined. The equilibria are found to be unstable in a very limited range of compactness and proton optical depth. This particular instability is unlikely to be the cause of the observed variability of the compact sources and implies that it is possible to build up high pair densities by a thermal mechanism in two temperature environments. The most important result considers the effects of pairs on the structure of geometrically and effectively optically thin accretion disks. A new approach for solving for the equilibrium structure of the disks is presented. In effect, the pair equilibrium states are projected into the space spanned by the disk structure parameters. This allows a direct visualization of all possible disk solutions at once. Each solution profile needs to be calculated only once and a complete disk solution is obtained by a simple radial coordinate transformation. The disk solutions are thus seen to be scale free in terms of the radial coordinate as well as in terms of the mass of the central object and the accretion rate. Two particular disk solutions are given. It is shown that including electron-positron pairs in the disk structure calculations leads to a breakdown of the thin disk assumptions and that more detailed disk modeling is required before electron-positron pairs can be self-consistently included
Campbell, Dean J.; Brewer, Emily R.; Martinez, Keri A.; Fitzjarrald, Tamara J.
2017-01-01
The purpose of this laboratory experiment is to study fundamental concepts of kinetics and equilibria and the isotope effects associated with both of these concepts. The concepts of isotopes in introductory and general chemistry courses are typically used within the contexts of atomic weights and radioactivity. Kinetic and equilibrium isotope…
Re-analysis of exponential rigid-rotor astron equilibria
International Nuclear Information System (INIS)
Lovelace, R.V.; Larrabee, D.A.; Fleischmann, H.H.
1978-01-01
Previous studies of exponential rigid-rotor astron equilibria include particles which are not trapped in the self-field of the configuration. The modification of these studies required to exclude untrapped particles is derived
Surface current equilibria from a geometric point of view
International Nuclear Information System (INIS)
Kaiser, R.; Salat, A.
1993-04-01
This paper addresses the inverse problem of the existence of surface current MHD equilibria in toroidal geometry with vanishing magnetic field inside. Inverse means that the plasma-vacuum interface rather than the external wall or conductors are given and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: What toroidal surfaces with analytic parameterization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering and are described by a function satisfying a nonlinear partial differential equation of the Hamilton-Jacobi type whose coefficients are combinations of the metric elements of the surface. All known equilibria - equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform - turn out to be solutions of separable cases of that equation and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behaviour of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry KAM-type behaviour is observed, i.e. destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry an analytic criterion is
Field line diversion properties of finite β-helias equilibria
International Nuclear Information System (INIS)
Hayashi, Takaya; Schwenn, Ulrich; Strumberger, Erika.
1992-01-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite pressure equilibria. The results indicate that a divertor concept which has been developed from the diversion properties of the corresponding vacuum field can be maintained for finite pressure equilibria. Cross-field particle transport is simulated by a simplified scrape-off layer (SOL) model. (author)
Acquisition and evaluation of thermodynamic data for morenosite-retgersite equilibria at 0.1 MPa
Chou, I.-Ming; Seal, R.R.
2003-01-01
Metal-sulfate salts in mine drainage environments commonly occur as solid solutions containing Fe, Cu, Mg, Zn, Al, Mn, Ni, Co, Cd, and other elements. Thermodynamic data for some of the end-member salts containing Fe, Cu, Zn, and Mg have been collected and evaluated previously, and the present study extends to the system containing Ni. Morenosite (NiSO4-7H2O)-retgersite (NiSO4-6H2O) equilibria were determined along five humidity buffer curves at 0.1 MPa and between 5 and 22??C. Reversals along these humidity-buffer curves yield In K = 17.58-6303.35/T, where K is the equilibrium constant, and T is temperature in K. The derived standard Gibbs free energy of reaction is 8.84 kJ/mol, which agrees very well with the values of 8.90, 8.83, and 8.85 kJ/mol based on the vapor pressure measurements of Schumb (1923), Bonnell and Burridge (1935), and Stout et al. (1966). respectively. This value also agrees reasonably well with the values of 8.65 and 9.56 kJ/mol calculated from the data compiled by Wagman et al. (1982) and DeKock (1982), respectively. The temperature-humidity relationships defined by this study for dehydration equilibria between morenosite and retgersite explain the more common occurrence of retgersite relative to morenosite in nature.
Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent
2011-05-01
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society
Evaluation of Thermodynamic Models for Predicting Phase Equilibria of CO2 + Impurity Binary Mixture
Shin, Byeong Soo; Rho, Won Gu; You, Seong-Sik; Kang, Jeong Won; Lee, Chul Soo
2018-03-01
For the design and operation of CO2 capture and storage (CCS) processes, equation of state (EoS) models are used for phase equilibrium calculations. Reliability of an EoS model plays a crucial role, and many variations of EoS models have been reported and continue to be published. The prediction of phase equilibria for CO2 mixtures containing SO2, N2, NO, H2, O2, CH4, H2S, Ar, and H2O is important for CO2 transportation because the captured gas normally contains small amounts of impurities even though it is purified in advance. For the design of pipelines in deep sea or arctic conditions, flow assurance and safety are considered priority issues, and highly reliable calculations are required. In this work, predictive Soave-Redlich-Kwong, cubic plus association, Groupe Européen de Recherches Gazières (GERG-2008), perturbed-chain statistical associating fluid theory, and non-random lattice fluids hydrogen bond EoS models were compared regarding performance in calculating phase equilibria of CO2-impurity binary mixtures and with the collected literature data. No single EoS could cover the entire range of systems considered in this study. Weaknesses and strong points of each EoS model were analyzed, and recommendations are given as guidelines for safe design and operation of CCS processes.
Watts, David
This dissertation studies electricity markets based on two-settlement systems and applies the concept of conjectural variation (CV) as a tool for representing different levels of competitiveness in the market. Some recent theoretical works are addressed to support the use of CV as a solution concept. A notion of consistency is introduced to make the level of competitiveness of the market endogenous, and allows finding consistent CV equilibria and the corresponding conditions for existence of equilibria. First, a case is studied in which firms hold exogenous levels of forward commitments. Then, backward induction and sub-game perfection are used to solve sequentially for the spot and forward market equilibrium. This allows analyzing how firms take positions in the forward market, based on considering their later impact on the spot market. It is concluded that positions taken in the forward market depend largely on firms expectations about the competitiveness of both the spot and the forward market. Forward markets are welfare enhancing even if they are not as competitive as the associated spot market as long as they are not too oligopolistie. The above formulation is used to model a dynamic scenario to analyze market stability, linking this research to Dr. Alvarado's earlier research on market stability. This brings about interesting trade offs between market power and market stability.
Phase equilibria in the BaUO3-BaZrO3-BaMoO3 system
International Nuclear Information System (INIS)
Kurosaki, Ken; Yamanaka, Shinsuke; Matsuda, Tetsushi; Uno, Masayoshi; Yamamoto, Kazuya; Namekawa, Takashi
2002-01-01
The phase equilibria in the pseudo-ternary BaUO 3 -BaZrO 3 -BaMoO 3 system were studied to understand the thermochemical properties of the perovskite type gray oxide phase in high burnup MOX fuel. Thermodynamic equilibrium calculation for the system was performed by using a Chem Sage program under the various oxygen potentials. Solid solutions existing in the system were treated by an ideal solution model. The present calculation results well agreed with the previous reported post irradiation examination results, showing that BaMoO 3 was scarcely included in the gray oxide phase. (author)
International Nuclear Information System (INIS)
Li Xiaoli; Tamura, Kazuhiro
2010-01-01
(Ternary liquid + liquid) equilibria (tie-lines) of (water + acetone + α-pinene) at T = (288.15, 298.15, and 308.15) K and (water + acetone + β-pinene, or limonene) at T = 298.15 K have been measured. The experimental (ternary liquid + liquid) equilibrium data have been correlated successfully by the original UNIQUAC and modified UNIQUAC models. The modified UNIQUAC model reproduced accurately the experimental results for the (water + acetone + α-pinene) system at all the temperatures but fairly agreed with the experimental data for the (water + acetone + β-pinene, or limonene) systems.
Phase equilibria in chemical reactive fluid mixtures
International Nuclear Information System (INIS)
Maurer, Gerd
2011-01-01
Downstream processing is a major part of nearly all processes in the chemical industries. Most separation processes in the chemical (and related) industries for fluid mixtures are based on phase equilibrium phenomena. The majority of separation processes can be modelled assuming that chemical reactions are of no (or very minor) importance, i.e., assuming that the overall speciation remains unchanged during a separation process. However, there are also a large number of industrially important processes where the thermodynamic properties are influenced by chemical reactions. The phase equilibrium of chemical reactive mixtures has been a major research area of the author's group over nearly 40 years. In this contribution, three examples from that research are discussed. The first example deals with the vapour phase dimerisation of carboxylic acids and its consequences on phase equilibrium phenomena and phase equilibrium predictions. The second example deals with the solubility of sour gases (e.g., carbon dioxide and sulfur dioxide) in aqueous solutions of ammonia. That topic has been of interest for many years, e.g., in relation with the gasification and liquefaction of coal and, more recently, with the removal of carbon dioxide from flue gas in the 'chilled ammonia process'. The third example deals with phase equilibrium phenomena in aqueous solutions of polyelectrolytes. It deals with the phenomenon of 'counter ion condensation' and methods to model the Gibbs free energy of such solutions.
The truthful signalling hypothesis: an explicit general equilibrium model.
Hausken, Kjell; Hirshleifer, Jack
2004-06-21
In mating competition, the truthful signalling hypothesis (TSH), sometimes known as the handicap principle, asserts that higher-quality males signal while lower-quality males do not (or else emit smaller signals). Also, the signals are "believed", that is, females mate preferentially with higher-signalling males. Our analysis employs specific functional forms to generate analytic solutions and numerical simulations that illuminate the conditions needed to validate the TSH. Analytic innovations include: (1) A Mating Success Function indicates how female mating choices respond to higher and lower signalling levels. (2) A congestion function rules out corner solutions in which females would mate exclusively with higher-quality males. (3) A Malthusian condition determines equilibrium population size as related to per-capita resource availability. Equilibria validating the TSH are achieved over a wide range of parameters, though not universally. For TSH equilibria it is not strictly necessary that the high-quality males have an advantage in terms of lower per-unit signalling costs, but a cost difference in favor of the low-quality males cannot be too great if a TSH equilibrium is to persist. And although the literature has paid less attention to these points, TSH equilibria may also fail if: the quality disparity among males is too great, or the proportion of high-quality males in the population is too large, or if the congestion effect is too weak. Signalling being unprofitable in aggregate, it can take off from a no-signalling equilibrium only if the trait used for signalling is not initially a handicap, but instead is functionally useful at low levels. Selection for this trait sets in motion a bandwagon, whereby the initially useful indicator is pushed by male-male competition into the domain where it does indeed become a handicap.
Ion exchange equilibrium constants
Marcus, Y
2013-01-01
Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and
Quantity Constrained General Equilibrium
Babenko, R.; Talman, A.J.J.
2006-01-01
In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values.In case of price restrictions a general equilibrium may not exist and rationing on net demands or supplies is needed to clear the markets.In
ORMEC: a three-dimensional MHD spectral inverse equilibrium code
International Nuclear Information System (INIS)
Hirshman, S.P.; Hogan, J.T.
1986-02-01
The Oak Ridge Moments Equilibrium Code (ORMEC) is an efficient computer code that has been developed to calculate three-dimensional MHD equilibria using the inverse spectral method. The fixed boundary formulation, which is based on a variational principle for the spectral coefficients (moments) of the cylindrical coordinates R and Z, is described and compared with the finite difference code BETA developed by Bauer, Betancourt, and Garabedian. Calculations for the Heliotron, Wendelstein VIIA, and Advanced Toroidal Facility (ATF) configurations are performed to establish the accuracy and mesh convergence properties for the spectral method. 16 refs., 13 figs
Phase equilibria of didecyldimethylammonium nitrate ionic liquid with water and organic solvents
International Nuclear Information System (INIS)
Domanska, Urszula; Lugowska, Katarzyna; Pernak, Juliusz
2007-01-01
The phase diagrams for binary mixtures of an ammonium ionic liquid, didecyldimethylammonium nitrate, [DDA][NO 3 ], with: alcohols (propan-1-ol, butan-1-ol, octan-1-ol, and decan-1-ol): hydrocarbons (toluene, propylbenzene, hexane, and hexadecane) and with water were determined in our laboratory. The phase equilibria were measured by a dynamic method from T 220 K to either the melting point of the ionic liquid, or to the boiling point of the solvent. A simple liquidus curve in a eutectic system was observed for [DDA][NO 3 ] with: alcohols (propan-1-ol, butan-1-ol, and octan-1-ol); aromatic hydrocarbons (toluene and propylbenzene) and with water. (Solid + liquid) equilibria with immiscibility in the liquid phase were detected with the aliphatic hydrocarbons heptane and hexadecane and with decan-1-ol. (Liquid + liquid) equilibria for the system [DDA][NO 3 ] with hexadecane was observed for the whole mole fraction range of the ionic liquid. The observation of the upper critical solution temperature in binary mixtures of ([DDA][NO 3 ] + decan-1-ol, heptane, or hexadecane) was limited by the boiling temperature of the solvent. Characterisation and purity of the compounds were determined by elemental analysis, water content (Fisher method) and differential scanning microcalorimetry (d.s.c.) analysis. The d.s.c. method of analysis was used to determine melting temperatures and enthalpies of fusion. The thermal stability of the ionic liquid was resolved by the thermogravimetric technique-differential thermal analysis (TG-DTA) technique over a wide temperature range from (200 to 780) K. The thermal decomposition temperature of 50% of the sample was greater than 500 K. The (solid + liquid) phase equilibria, curves were correlated by means of different G Ex models utilizing parameters derived from the (solid + liquid) equilibrium. The root-mean-square deviations of the solubility temperatures for all calculated data are dependent upon the particular system and the particular
International Nuclear Information System (INIS)
Okano, K.; Ogawa, Y.; Naitou, H.
1988-07-01
A new MHD-equilibrium/current-drive analysis code was developed to analyse the high beta tokamak equilibria consistent with the beam driven current profiles. In this new code, the critical beta equilibrium, which is stable against the ballooning mode, the kink mode and the Mercier mode, is determined first using MHD equilibrium and stability analysis codes (EQLAUS/ERATO). Then, the current drive parameters and the plasma parameters, required to sustain this critical beta equilibrium, are determined by iterative calculations. The beam driven current profiles are evaluated by the Fokker-Planck calculations on individual flux surfaces, where the toroidal effects on the beam ion and plasma electron trajectories are considered. The pressure calculation takes into account the beam ion and fast alpha components. A peculiarity of our new method is that the obtained solution is not only consistent with the MHD equilibrium but also consistent with the critical beta limit conditions, in the current profile and the pressure profile. Using this new method, β ∼ 21 % bean and β ∼ 6 % D-type critical beta equilibria were scanned for various parameters; the major radius, magnetic field, temperature, injection energy, etc. It was found that the achievable Q value for the bean type was always about 30 % larger than for the D-type cases, where Q = fusion power/beam power. With strong beanness, Q ∼ 6 for DEMO type tokamaks (∼500 MWth) and Q ∼ 20 for power reactor size (4.5 GWth) are achievable. On the other hand, the Q value would not exceed sixteen for the D-type machines. (author)
International Nuclear Information System (INIS)
Byun, Hun-Soo
2016-01-01
Experimental data are reported on the phase equilibrium of propoxylated neopentyl glycol diacrylate in supercritical carbon dioxide. Phase equilibria data were measured in static method at a temperature of (313.2, 333.2, 353.2, 373.2 and 393.2) K and at pressures up to 27.82 MPa. At a constant pressure, the solubility of propoxylated neopentyl glycol diacrylate for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system increases as temperature increases. The (carbon dioxide + propoxylated neopentyl glycol diacrylate) system exhibits type-I phase behavior. The experimental result for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system is correlated with Peng- Robinson equation of state using mixing rule. The critical property of propoxylated neopentyl glycol diacrylate is predicted with Joback and Lyderson method
Accelerated convergence of the steepest-descent method for magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Handy, C.R.; Hirshman, S.P.
1984-06-01
Iterative schemes based on the method of steepest descent have recently been used to obtain magnetohydrodynamic (MHD) equilibria. Such schemes generate asymptotic geometric vector sequences whose convergence rate can be improved through the use of the epsilon-algorithm. The application of this nonlinear recursive technique to stiff systems is discussed. In principle, the epsilon-algorithm is capable of yielding quadratic convergence and therefore represents an attractive alternative to other quadratic convergence schemes requiring Jacobian matrix inversion. Because the damped MHD equations have eigenvalues with negative real parts (in the neighborhood of a stable equilibrium), the epsilon-algorithm will generally be stable. Concern for residual monotonic sequences leads to consideration of alternative methods for implementing the algorithm
Energy Technology Data Exchange (ETDEWEB)
Byun, Hun-Soo [Chonnam National University, Yeosu (Korea, Republic of)
2016-04-15
Experimental data are reported on the phase equilibrium of propoxylated neopentyl glycol diacrylate in supercritical carbon dioxide. Phase equilibria data were measured in static method at a temperature of (313.2, 333.2, 353.2, 373.2 and 393.2) K and at pressures up to 27.82 MPa. At a constant pressure, the solubility of propoxylated neopentyl glycol diacrylate for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system increases as temperature increases. The (carbon dioxide + propoxylated neopentyl glycol diacrylate) system exhibits type-I phase behavior. The experimental result for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system is correlated with Peng- Robinson equation of state using mixing rule. The critical property of propoxylated neopentyl glycol diacrylate is predicted with Joback and Lyderson method.
Phase equilibria and critical phenomena in the cesium nitrate-water-diethylamine ternary system
International Nuclear Information System (INIS)
Il'in, K.K.; Kurskij, V.F.; Cherkasov, D.G.
2008-01-01
Phase equilibria and critical events in ternary cesium nitrate-water-diethylamine system, where border binary liquid system is characterized by aliquation with lower critical temperature of solution (LCTS), have been investigated by visual-polythermal method in the 60-150 Deg C range. Interaction of cesium nitrate in the water-diethylamine system leads to lowering of its LCTS from 146.1 to 69.3 Deg C and decrease of mutual solubility. Distribution ratios of diethylamine between water and organic phases of monotectic equilibrium are calculated at different temperatures. Diethylamine salting out from aqueous solutions by cesium nitrates becomes stronger with rising temperature. Plotted isotherms of phase confirms generalized scheme of topological transformations of ternary systems phase diagrams: salt-binary solvent with salting out
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.
Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions
International Nuclear Information System (INIS)
Holm, D.D.
1985-08-01
Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs
Influence of somatic cell count on mineral content and salt equilibria of milk
Directory of Open Access Journals (Sweden)
Primo Mariani
2010-01-01
Full Text Available Aim of this research was to study the effect of somatic cell count on mineral content and salt equilibria at the level of quarter milk samples. Ten Italian Friesian cows, in which two homologous quarters (front quarters in 1 cow, rear quarters in 6 cows and both rear and front quarters in 3 cows were characterised by a milk SCC400,000 cells/mL (HC-milk, respectively, were selected. Cows were milked at quarter level during the morning milking and a single sample was collected from each selected quarter, thus, 26 quarter milk samples were collected. Compared to LC-milk, HC-milk was characterised by a lower content of phosphorus and potassium and by a higher content of both sodium and chloride. The equilibrium of calcium, phosphorus and magnesium between the colloidal and soluble phase of milk and the mineralisation degree of the casein micelles, were not different between HC and LC milk.
Prediction of phase equilibria in the In–Sb–Pb system
Directory of Open Access Journals (Sweden)
DUSKO MINIC
2008-03-01
Full Text Available Binary thermodynamic data, successfully used for phase diagram calculations of the binary systems In–Sb, Pb–Sb and In–Pb, were used for the prediction of the phase equilibria in the ternary In–Sb–Pb system. The predicted equilibrium phase diagram of the vertical Pb–InSb section was compared with the results of differential thermal analysis DTA and optical microscopy. The calculated phase diagram of the isothermal section at 300 °C was compared with the experimentally (SEM, EDX determined composition of phases in the chosen alloys after annealing. Very good agreement between the binary-based thermodynamic prediction and the experimental data was found in all cases. The calculated liquidus projection of the ternary In–Sb–Pb system is also presented.
International Nuclear Information System (INIS)
Perona, J.J.
1992-01-01
Chabazite zeolites are used at ORNL for decontamination of wastewaters containing 90 Sr and 137 Cs. Treatability studies have shown that chabazite can remove trace amounts of these nuclides from wastewaters containing much higher concentrations of calcium and magnesium. The design of ion exchange columns for multicomponent systems requires a method for predicting multicomponent equilibria from binary or ternary experiments, since the number of experiments required for an empirical equilibrium model is generally not feasible. Binary interaction parameters for the Wilson equation were used to predict solid-phase activity coefficients for the five-component system, and the sum of squares of deviations between experimental and predicted solution concentrations for the data points available was calculated. The average deviation per data point for the five-component system was about the same as for the calcium-magnesium-sodium ternary system
Optimization, Monotonicity and the Determination of Nash Equilibria — An Algorithmic Analysis
Lozovanu, D.; Pickl, S. W.; Weber, G.-W.
2004-08-01
This paper is concerned with the optimization of a nonlinear time-discrete model exploiting the special structure of the underlying cost game and the property of inverse matrices. The costs are interlinked by a system of linear inequalities. It is shown that, if the players cooperate, i.e., minimize the sum of all the costs, they achieve a Nash equilibrium. In order to determine Nash equilibria, the simplex method can be applied with respect to the dual problem. An introduction into the TEM model and its relationship to an economic Joint Implementation program is given. The equivalence problem is presented. The construction of the emission cost game and the allocation problem is explained. The assumption of inverse monotony for the matrices leads to a new result in the area of such allocation problems. A generalization of such problems is presented.
Poloidal field coil design for known plasma equilibrium states
International Nuclear Information System (INIS)
Paulson, C.C.; Todd, A.M.M.; Reusch, M.F.
1986-01-01
The technique for obtaining plasma equilibria with given boundary conditions has long been known and understood. The inverse problem of obtaining a poloidal field (PF) coil system from a given plasma equilibrium has been widely studied, however its solution has remained largely an art form. An investigation, by the writers, of this fundamentally ill-posed inverse problem has resulted in a new understanding of the requirements that solutions must satisfy. A set of interacting computer codes has been written which may be used to successfully design PF coil systems capable of supporting given plasma equilibria. It is shown that for discrete coil systems with a reasonable number of elements the standard minimization of the R M S flux error can lead to undesirable results. Examples are given to show that an additional stability requirement must be imposed on the regularization parameter to obtain correct solutions. For some equilibria, the authors find that the inverse problem admits dual solutions corresponding to two possible magnetic field configurations that fit the constraining relations on the plasma surface equally well. An additional minimization of the absolute value of the limiter flux is required to discriminate between these solutions
Adaptive Topographies and Equilibrium Selection in an Evolutionary Game
Osinga, Hinke M.; Marshall, James A. R.
2015-01-01
It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches. PMID:25706762
Formation and 'self-healing' of magnetic islands in finite-β Helias equilibria
International Nuclear Information System (INIS)
Hayashi, T.; Sato, T.; Merkel, P.; Nuehrenberg, J.; Schwenn, U.
1994-01-01
The behaviour of finite-pressure-induced magnetic islands is numerically analyzed for three-dimensional magnetohydrodynamic equilibria of the Helias configuration by using a three-dimensional equilibrium code. It is found that an island chain is generated on the 5/6 rational surface, when such a surface appears in the plasma region of the finite-β equilibrium. The island chain, however, is not so dangerous as to destroy the plasma confinement even if it appears in a vanishingly small shear region. Thus, a high β equilibrium with clear magnetic surfaces can be realized. Moreover, it is definitely confirmed that the finite pressure effect sometimes exhibits an unexpectedly good aspect, namely, that the vacuum islands are removed as β increases, which can be called 'self-healing' of islands. This property can be explained by the numerically discovered fact that the phases of islands induced by the finite-pressure effect are always locked in the same phase regardless of β. (author)
Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures
International Nuclear Information System (INIS)
Cremaschini, Claudio; Stuchlík, Zdeněk
2014-01-01
The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed
International Nuclear Information System (INIS)
Park, Joo Hyun; Kim, Dong Sik; Kim, Yong Hwan; Lee, Sang Beom
2005-01-01
A thermodynamic equilibrium between aluminum and oxygen along with the inclusion morphology in Fe-16%Cr stainless steel was investigated to understand the fundamentals of aluminum deoxidation technology for ferritic stainless steels. Further, the effects of calcium addition on the changes in chemistry and morphology of inclusions were discussed. The measured results for aluminum-oxygen equilibria exhibit relatively good agreement with the calculated values, indicating that the introduction of the first- and second-order interaction parameters, recently reported, is reasonable to numerically express aluminum deoxidation equilibrium in a ferritic stainless steel. In the composition of dissolved aluminum content greater than about 60 ppm, pure alumina particles were observed, while the alumino-manganese silicates containing Cr 2 O 3 were appeared at less than 20 mass ppm of dissolved aluminum. The formation of calcium aluminate inclusions after Ca treatment could be discussed based on the thermodynamic equilibrium with calcium, aluminum, and oxygen in the steel melts. In the composition of steel melt with relatively high content of calcium and low aluminum, the log(X CaO /X Al 2 O 3 ) of inclusions linearly increases with increasing the log [a Ca /a Al 2 ·a O 2 ] with the slope close to unity. However, the slope of the line is significantly lower than the expected value in the composition of steel melt with relatively low calcium and high aluminum contents
Model for ICRF fast wave current drive in self-consistent MHD equilibria
International Nuclear Information System (INIS)
Bonoli, P.T.; Englade, R.C.; Porkolab, M.; Fenstermacher, M.E.
1993-01-01
Recently, a model for fast wave current drive in the ion cyclotron radio frequency (ICRF) range was incorporated into the current drive and MHD equilibrium code ACCOME. The ACCOME model combines a free boundary solution of the Grad Shafranov equation with the calculation of driven currents due to neutral beam injection, lower hybrid (LH) waves, bootstrap effects, and ICRF fast waves. The equilibrium and current drive packages iterate between each other to obtain an MHD equilibrium which is consistent with the profiles of driven current density. The ICRF current drive package combines a toroidal full-wave code (FISIC) with a parameterization of the current drive efficiency obtained from an adjoint solution of the Fokker Planck equation. The electron absorption calculation in the full-wave code properly accounts for the combined effects of electron Landau damping (ELD) and transit time magnetic pumping (TTMP), assuming a Maxwellian (or bi-Maxwellian) electron distribution function. Furthermore, the current drive efficiency includes the effects of particle trapping, momentum conserving corrections to the background Fokker Planck collision operator, and toroidally induced variations in the parallel wavenumbers of the injected ICRF waves. This model has been used to carry out detailed studies of advanced physics scenarios in the proposed Tokamak Physics Experiment (TPX). Results are shown, for example, which demonstrate the possibility of achieving stable equilibria at high beta and high bootstrap current fraction in TPX. Model results are also shown for the proposed ITER device
Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio; Stuchlík, Zdeněk [Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava (Czech Republic)
2014-04-15
The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.
A novel grid multiwing chaotic system with only non-hyperbolic equilibria
Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le
2018-05-01
The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.
Axisymmetric plasma equilibria in a Kerr metric
Elsässer, Klaus
2001-10-01
Plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species. The quasi-neutrality assumption (no charge density, no toroidal current) allows to solve Maxwell's equations analytically for any axisymmetric stationary metric, and to reduce the fluid equations to one single scalar equation for the stream function \\chi of the positrons or ions, respectively. The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The \\chi-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Axisymmetric Plasma Equilibria in General Relativity
Elsässer, Klaus
Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the rôle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio me/mi. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
One-electron transfer equilibria and redox potentials of radicals studied by pulse radiolysis
International Nuclear Information System (INIS)
Meisel, D.; Czapski, G.
1975-01-01
The pulse radiolysis technique is utilized for measurements of the equilibrium constants for electron transfer between the durosemiquinone radical anion and oxygen, menadione, and indigodisulfonate. These equilibrium constants are in turn used for calculations of one-electron redox potentials for these systems. Each of these equilibrium constants was determined experimentally and independently and found to be self-consistent. Only for the reactions of the semiquinone radical ions with oxygen could the electron transfer reaction be followed directly. For the reactions between the various quinone-semiquinone systems substantial indirect evidence is presented that these equilibria are achieved rapidly. In those cases equilibrium constants were determined from studies of the effect of quinone concentrations on the relative yields of the semiquinones. A method for distinguishing between kinetic competition and equilibrium is outlined and its usefulness is emphasized. The DQ parallel DQ - (DQ = duroquinone) and IDS parallel IDS - (IDS = indigodisulfonate) systems were employed as reference couples as the redox potentials for those systems are either available in the literature (IDS parallel IDS - ) or may be calculated from available data (DQ parallel DQ - ). Taking E 7 1 , the redox potential for the first one-electron reduction step at pH 7, of DQ parallel DQ - as -0.235 V or of IDS parallelIDS - as -0.247 V both yield E 7 1 = -0.325 V for the O 2 parallel O 2 - system (1 atm of O 2 ) and E 2 1 = -0.20 V for the menadione system. (U.S.)
Quasi-equilibria in reduced Liouville spaces.
Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon
2012-06-14
The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.
Perturbed solutions of fixed boundary MHD equilibria
International Nuclear Information System (INIS)
Portone, A.
2004-01-01
In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)
Isotope effects in ion-exchange equilibria in aqueous and mixed solvent systems
International Nuclear Information System (INIS)
Gupta, A.R.
1979-01-01
Isotope effects in ion-exchange equilibria in aqueous and mixed solvents are analyzed in terms of the general features of ion-exchange equilibria and of isotope effects in chemical equilibria. The special role of solvent fractionation effects in ion-exchange equilibria in mixed solvents is pointed out. The various situations arising in isotope fractionation in ion exchange in mixed solvents due to solvent fractionation effects are theoretically discussed. The experimental data on lithium isotope effects in ion-exchange equilibria in mixed solvents are shown to conform to the above situations. The limitations of ion-exchange equilibria in mixed solvents for isotope fractionation are pointed out. 3 tables
DEFF Research Database (Denmark)
Hansen, Poul Erik; Borisov, Eugeny V.; Lindon, John C.
2015-01-01
The tautomeric equilibria for 2-pyridoyl-, 3-pyridoyl-, and 4-pyridoyl-benzoyl methane have been investigated using deuterium isotope effects on 1H and 13C chemical shifts both in the liquid and the solid state. Equilibria are established both in the liquid and the solid state. In addition......, in the solution state the 2-bond and 3-bond J(1H–13C) coupling constants have been used to confirm the equilibrium positions. The isotope effects due to deuteriation at the OH position are shown to be superior to chemical shift in determination of equilibrium positions of these almost symmetrical -pyridoyl......-benzoyl methanes. The assignments of the NMR spectra are supported by calculations of the chemical shifts at the DFT level. The equilibrium positions are shown to be different in the liquid and the solid state. In the liquid state the 4-pyridoyl derivative is at the B-form (C-1 is OH), whereas the 2-and 3-pyridoyl...
Equilibrium and stability studies for high beta plasmas in torsatron/heliotron devices
International Nuclear Information System (INIS)
Carreras, B.A.; Cooper, W.A.; Charlton, L.A.
1983-01-01
The equilibrium and stability properties of high β plasmas in torsatron/heliotron devices have been investigated. Three numerical approaches have been used to study plasma equilibria for a range of coil configurations. The method of averaging permits fast equilibrium and stability calculations. Two fully 3-D codes, namely the Chodura-Schluter code, and the NEAR code recently developed at ORNL, are used to explore selected regions of parameter space. The resulting equilibria calculated with different methods are in good agreement. This validates the average method approach and enhances its usefulness. Results are presented for configurations with different aspect ratios and number of field periods. The role of the vertical field has also been studied in detail. The main conclusion is that for moderate aspect ratios (Asub(p) <= 8), the self-stabilizing effect of the magnetic axis shift is large enough to open a direct path to the second stability regime. (author)
Analysis of equilibrium about bidding strategy of suppliers with future contracts
International Nuclear Information System (INIS)
Yuan, Zhiqiang; Liu, Dong; Jiang, Chuanwen
2007-01-01
In this paper, the supply function model is employed to simulate the bidding strategy of suppliers in the power pool, and models of the supply function with future contracts are presented. It is proved that only one of the parameters between slope and intercept of the bidding curve is an independent variable in order to achieve definite equilibrium. In the meantime, the equilibria of the bidding strategy about suppliers are studied when different intercepts of the bidding curve are chosen. Some examples are employed to study the Nash equilibrium strategies of suppliers with different future contracts in various bidding strategy models. The results show that the equilibria are different in different bidding strategy models, but the future contracts can effectively make spot prices decrease in all the models
Equilibrium and stability studies for high-beta plasmas in torsatron/heliotron devices
International Nuclear Information System (INIS)
Carreras, B.A.; Charlton, L.A.; Cooper, W.A.
1983-01-01
The equilibrium and stability properties of high-#betta# plasmas in torsatron/heliotron devices have been investigated. Three numerical approaches have been used to study plasma equilibria for a range of coil configurations. The method of averaging permits fast equilibrium and stability calculations. Two fully 3-D codes, namely the Chodura-Schluter code, and the NEAR code recently developed at ORNL, are used to explore selected regions of parameter space. The resulting equilibria calculated with different methods are in good agreement. This validates the average method approach and enhances its usefulness. Results are presented for configurations with different aspect ratios and number of field periods. The role of the vertical field has also been studied in detail. The main conclusion is that for moderate aspect ratios (A/sub p/ less than or equal to 8), the self-stabilizing effect of the magnetic-axis shift is large enough to open a direct path to the second-stability regime
Thermal equilibrium of pure electron plasmas across a central region of magnetic surfaces
Hahn, Michael; Pedersen, Thomas Sunn
2009-06-01
Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium.
Thermal equilibrium of pure electron plasmas across a central region of magnetic surfaces
International Nuclear Information System (INIS)
Hahn, Michael; Pedersen, Thomas Sunn
2009-01-01
Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium.
Brand Loyalty and Market Equilibrium
Birger Wernerfelt
1991-01-01
Two concepts of brand loyalty are defined, “inertial” brand loyalty resulting from time lags in awareness, and “cost-based” brand loyalty resulting from intertemporal utility effects. Their market level implications are formally derived in a continuous time model. It is found that inertial brand loyalty leads to equilibria with price dispersion, while cost-based brand loyalty also may allow single price equilibria. In all cases, as brand loyalty vanishes, so does the difference between the av...
Gyrokinetic statistical absolute equilibrium and turbulence
International Nuclear Information System (INIS)
Zhu Jianzhou; Hammett, Gregory W.
2010-01-01
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
Gyrokinetic Statistical Absolute Equilibrium and Turbulence
International Nuclear Information System (INIS)
Zhu, Jian-Zhou; Hammett, Gregory W.
2011-01-01
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence (T.-D. Lee, 'On some statistical properties of hydrodynamical and magnetohydrodynamical fields,' Q. Appl. Math. 10, 69 (1952)) is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
Persat, Alexandre; Chambers, Robert D; Santiago, Juan G
2009-09-07
We review fundamental and applied acid-base equilibrium chemistry useful to microfluidic electrokinetics. We present elements of acid-base equilibrium reactions and derive rules for pH calculation for simple buffers. We also present a general formulation to calculate pH of more complex, arbitrary mixtures of electrolytes, and discuss the effects of ionic strength and temperature on pH calculation. More practically, we offer advice on buffer preparation and on buffer reporting. We also discuss "real world" buffers and likely contamination sources. In particular, we discuss the effects of atmospheric carbon dioxide on buffer systems, namely, the increase in ionic strength and acidification of typical electrokinetic device buffers. In Part II of this two-paper series, we discuss the coupling of acid-base equilibria with electrolyte dynamics and electrochemistry in typical microfluidic electrokinetic systems.
Analytic description of tokamak equilibrium sustained by high fraction bootstrap current
International Nuclear Information System (INIS)
Shi Bingren
2002-01-01
Recently, to save the current drive power and to obtain more favorable confinement merit for tokamak reactor, large faction bootstrap current sustained equilibrium has attracted great interests both theoretically and experimentally. An powerful expanding technique and the tokamak ordering are used to expand the Grad-Shafranov equation to obtain a series of ordinary differential equations which allow for different sets of input parameters. The fully bootstrap current sustained tokamak equilibria are then solved analytically
Aggregation equilibria in arsenic doped silicon
International Nuclear Information System (INIS)
Derdour, M.; Furlan, G.; Nobili, D.
1993-08-01
Carrier density profile determinations are reported which confirm that a mass action relation holds between the ionized and the inactive mobile As in silicon. Experiments were performed under equilibrium conditions at temperatures in the range 780-885 deg. C. The carrier density n vs. the dopant concentration N T exhibits a very pronounced saturation behaviour which is compared with the one expected in well known cluster models. These results complement the recent finding that the inactive As can exist in equilibrium with the monoclinic SiAs. From this information and previous SAXS, TEM, and EXAFS results one can conclude that a pre-precipitation phenomenon, with its inherent cluster distribution, is responsible for the inactive As. (author). 21 refs, 2 figs
Kalai-Smorodinsky Bargaining Solution Equilibria
Giuseppe De Marco; Jacqueline Morgan
2009-01-01
Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the rel- ative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We pr...
(Liquid + liquid) equilibria of four alcohol–water systems containing 1,8-cineole at T = 298.15 K
International Nuclear Information System (INIS)
Li, Hengde; Feng, Zhangni; Wan, Li; Huang, Cheng; Zhang, Tianfei; Fang, Yanxiong
2016-01-01
Graphical abstract: (Liquid + liquid) equilibria of C_1–C_4 alcohol–water systems containing 1,8-cineole are presented. Distribution ratios of alcohol in the mixtures are examined. The immiscible region of the LLE systems is evaluated and discussed. - Highlights: • Ternary (liquid + liquid) equilibria containing 1,8-cineole are presented. • Distribution ratios of C_1–C_4 alcohol in the mixtures are examined. • The LLE values were correlated using the NRTL and UNIQUAC models. - Abstract: As an eco-friendly compound from essential oils, 1,8-cineole (cineole, eucalyptol) has the potential to replace the ozone depleting industrial solvents. This paper presents experimental (liquid + liquid) equilibrium (LLE) data for four alcohol–water systems containing 1,8-cineole. To evaluate the phase equilibrium properties of 1,8-cineole in aqueous alcohol mixtures, LLE values for the ternary systems (water + methanol or ethanol or 1-propanol or 1-butanol + 1,8-cineole) were determined with a tie-line method at T = 298.15 K under atmospheric pressure. The well-known Hand, Bachman and Othmer–Tobias equations were used to test the reliability of the experimental results. The binodal curves and distribution ratios of alcohol in the mixtures are shown and discussed. The experimental LLE values were satisfactorily correlated by the NRTL and UNIQUAC models.
International Nuclear Information System (INIS)
Balter, H.S.
1994-01-01
This work studies the behaviour of radionuclides when it produce a desintegration activity,decay and the isotopes stable creation. It gives definitions about the equilibrium between activity of parent and activity of the daughter, radioactive decay,isotope stable and transient equilibrium and maxim activity time. Some considerations had been given to generators that permit a disgregation of two radioisotopes in equilibrium and its good performance. Tabs
Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data
DEFF Research Database (Denmark)
Marcussen, Lis
2000-01-01
A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...
Equilibrium and perturbations in plasma-vacuum systems
International Nuclear Information System (INIS)
Mercier, C.
1974-01-01
Thermonuclear plasmas must be maintained far from all material contact. In order to realize this condition, one uses in the vacuum surrounding the plasma, a metal wall supposed perfectly conducting and currents whose positions and intensities have to be suitably chosen. The problem of equilibrium consists of finding a toroidal solution of the system of equations JxB=grad P, div B=0, J=rot B, B,J, and P being respectively the magnetic field, current intensity and plasma pressure. The problem can be solved in symmetry of revolution using cylindrical coordinates. The arrangement and intensity of the currents found will not be exactly realized due to, for exemple, technical reasons. Consequently, the first problem of equilibrium is considered as a first approximation and the configuration which will be obtained under imposed real conditions is computed as perturbed equilibria [fr
Outline of fast analyzer for MHD equilibrium 'FAME'
International Nuclear Information System (INIS)
Sakata, Shinya; Haginoya, Hirofumi; Tsuruoka, Takuya; Aoyagi, Tetsuo; Saito, Naoyuki; Harada, Hiroo; Tani, Keiji; Watanabe, Hideto.
1994-03-01
The FAME (Fast Analyzer for Magnetohydrodynamic (MHD) Equilibrium) system has been developed in order to provide more than 100 MHD equilibria in time series which are enough for the non-stationary analysis of the experimental data of JT-60 within about 20 minutes shot interval. The FAME is an MIMD type small scale parallel computer with 20 microprocessors which are connected by a multi-stage switching system. The maximum theoretical speed is 250 MFLOPS. For the software system of FAME, MHD equilibrium analysis code SELENE and its input data production code FBI are tuned up taking the parallel processing into consideration. Consequently, the computational performance of the FAME system becomes more than 7 times faster than the existing general purpose computer FACOM M780-10s. This report summarizes the outline of the FAME system including hardware, soft-ware and peripheral equipments. (author)
Ballooning mode second stability region for sequences of tokamak equilibria
International Nuclear Information System (INIS)
Sugiyama, L.; Mark, J.W.K.
A numerical study of several sequences of tokamak equilibria derived from two flux conserving sequences confirms the tendency of high n ideal MHD ballooning modes to stabilize for values of the plasma beta greater than a second critical beta, for sufficiently favorable equilibria. The major stabilizing effect of increasing the inverse rotational transform profile q(Psi) for equilibria with the same flux surface geometry is shown. The unstable region shifts toward larger shear d ln q/d ln γ and the width of the region measured in terms of the poloidal beta or a pressure gradient parameter, for fixed shear, decreases. The smaller aspect ratio sequences are more sensitive to changes in q and have less stringent limits on the attainable value of the plasma beta in the high beta stable region. Finally, the disconnected mode approximation is shown to provide a reasonable description of the second high beta stability boundary
Hydrostatic Equilibria of Rotating Stars with Realistic Equation of State
Yasutake, Nobutoshi; Fujisawa, Kotaro; Okawa, Hirotada; Yamada, Shoichi
Stars rotate generally, but it is a non-trivial issue to obtain hydrostatic equilibria for rapidly rotating stars theoretically, especially for baroclinic cases, in which the pressure depends not only on the density, but also on the temperature and compositions. It is clear that the stellar structures with realistic equation of state are the baroclinic cases, but there are not so many studies for such equilibria. In this study, we propose two methods to obtain hydrostatic equilibria considering rotation and baroclinicity, namely the weak-solution method and the strong-solution method. The former method is based on the variational principle, which is also applied to the calculation of the inhomogeneous phases, known as the pasta structures, in crust of neutron stars. We found this method might break the balance equation locally, then introduce the strong-solution method. Note that our method is formulated in the mass coordinate, and it is hence appropriated for the stellar evolution calculations.
Equilibrium states of nonsynchronous stars in detached binaries
International Nuclear Information System (INIS)
Lubow, S.H.
1979-01-01
The effects of nonsynchronous spin on equilibrium states for the radiative envelopes of detached members of close binaries are analyzed. With the adoption of the assumption that the nonsynchronous speeds, u, are much less than the relative orbital speed, Ωd, of the component stars, the full set of stellar structure equations, generalized to include the gas dynamical and heat transport effects of spin, are analyzed to linear order in u/Ωd. For these equilibria: (2) from this velocity field isobars and hence stellar shapes can be calculated for equilibrium states of slightly nonsynchronously rotating stars. On the orbit plane these surfaces coincide with the Roche equipotentials. (3) All sightly nonsynchronous equilibria are baroclinic. Isodensities and isotherms are inclined to isobars by an angle on the order of 0 0 .3 x (u/Ωd for a star in quasi-rigid rotation that nearly fills its Roche lobe). (4) The surface flux distribution departs from the usual gravity darkening law by an amount that scales with u/Ωd. Comparisons of this work are made with the results of previous investigations, and possibilities for future investigations are discussed
International Nuclear Information System (INIS)
Throumoulopoulos, G.N.; Tasso, H.
2003-01-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η (parallel) and η (perpendicular) parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η (parallel) (ψ) or η (perpendicular) (ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η (parallel) and η (perpendicular) profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η (perpendicular) >η (parallel) . For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI 2 /dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η (perpendicular) -η (parallel) for the reversed-field pinch scaling, B p ≅B t , is nearly two times larger than that for the tokamak scaling, B p ≅0.1B t (B p and B t are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of - but not inconsistent with - Pfirsch-Schlueter diffusion, indicate that
Throumoulopoulos, G. N.; Tasso, H.
2003-06-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.
Adaptive Equilibrium Regulation: A Balancing Act in Two Timescales
Boker, Steven M.
2015-01-01
An equilibrium involves a balancing of forces. Just as one maintains upright posture in standing or walking, many self-regulatory and interpersonal behaviors can be framed as a balancing act between an ever changing environment and within-person processes. The emerging balance between person and environment, the equilibria, are dynamic and adaptive in response to development and learning. A distinction is made between equilibrium achieved solely due to a short timescale balancing of forces and a longer timescale preferred equilibrium which we define as a state towards which the system slowly adapts. Together, these are developed into a framework that this article calls Adaptive Equilibrium Regulation (ÆR), which separates a regulatory process into two timescales: a faster regulation that automatically balances forces and a slower timescale adaptation process that reconfigures the fast regulation so as to move the system towards its preferred equilibrium when an environmental force persists over the longer timescale. This way of thinking leads to novel models for the interplay between multiple timescales of behavior, learning, and development. PMID:27066197
The stability of Z-pinches with equilibrium flows
International Nuclear Information System (INIS)
Howell, D.F.
1999-01-01
According to Ideal Magnetohydrodynamic (MHD) theory the Z-pinch is an inherently unstable magnetic configuration. However it is possible that there exist regimes of operation whereby the predicted instabilities may be reduced or even eliminated. We must look to effects normally ignored in the Ideal MHD model in order to predict such regimes. In this thesis various non-ideal effects will be studied, namely the inclusion of equilibrium flow and finite Larmor radius effects. Astrophysical jets, for example those seen to be emitted from active galactic nuclei, are seen to persist for a greater time than suggested by Ideal MHD before the onset of instabilities. It is postulated that one of the contributing factors to this enhanced stability is the presence of a sheared axial flow. In this thesis we study the stability properties of the Z-pinch where flow is present in the equilibrium. It is found that a sheared axial flow generally has a stabilising effect, the degree of which is determined by the equilibrium and flow profiles, but that absolute stability cannot be achieved due to the onset of the Kelvin-Helmholtz instability. The effect of adding rotation has also been studied. It is found that adding rotation changes the equilibrium density profiles from the static case, and that it always has a destabilising effect. Another postulated method of stabilising the Z-pinch is by increasing the ratio of the ion Larmor radius to the pinch radius, and it is seen to have a stabilising effect for some equilibria in the collisionless regime. In this thesis we study the effects of increasing the Larmor radius in the collisional regime using the Hall fluid model. It is found that for free boundary modes the stability properties are unchanged for experimentally realistic values of the Larmor radius, but for fixed boundary modes a small stabilising effect is noted for some equilibria. (author)
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Ideal MHD beta-limits of poloidally asymmetric equilibria
International Nuclear Information System (INIS)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in β/sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is β/sub critical/ approx. = 6.5%
Nash Equilibria in Symmetric Graph Games with Partial Observation
DEFF Research Database (Denmark)
Bouyer, Patricia; Markey, Nicolas; Vester, Steen
2017-01-01
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information...... and symmetry constraints, which make the computation of Nash equilibria difficult. We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria for qualitative objectives in this game model....
Nash Equilibria in Symmetric Games with Partial Observation
DEFF Research Database (Denmark)
Bouyer, Patricia; Markey, Nicolas; Vester, Steen
2014-01-01
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information...... and symmetry constraints, which make the computation of Nash equilibria difficult. We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria (for qualitative objectives) in this game model....
Recent progress in the relative equilibria of point vortices — In memoriam Hassan Aref
DEFF Research Database (Denmark)
Beelen, Peter; Brøns, Morten; Krishnamurthy, Vikas S.
2013-01-01
Hassan Aref, who sadly passed away in 2011, was one of the world's leading researchers in the dynamics and equilibria of point vortices. We review two problems on the subject of point vortex relative equilibria in which he was engaged at the time of his death: bilinear relative equilibria...
Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P.
2008-01-01
Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up
International Nuclear Information System (INIS)
Hudson, S.R.; Monticello, D.A.; Reiman, A.H.; Boozer, A.H.; Strickler, D.J.; Hirshman, S.P.; Zarnstorff, M.C.
2002-01-01
Magnetic islands in free-boundary stellarator equilibria are suppressed using a procedure that iterates the plasma equilibrium equations and, at each iteration, adjusts the coil geometry to cancel resonant fields produced by the plasma. The coils are constrained to satisfy certain measures of engineering acceptability and the plasma is constrained to ensure kink stability. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied with success to a candidate plasma and coil design for the National Compact Stellarator eXperiment [Physics of Plasma, 7 (2000) 1911
L. Braga, F.
2013-10-01
The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic (MHD) equilibrium with reversed current density (RCD) profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.
Phase equilibria at the Zirconium metal purification
International Nuclear Information System (INIS)
Dwiretnani-Sudjoko; Busron-Masduki; Sunardjo; Budi-Sulistyo
1996-01-01
It was investigated the research in the purification of zirconium metal, which was results from the reduction process, by adding heat in the vacuum environment. The process was done in batch in the stainless steel reactor, equiped with vacuum pump and electric heater. The investigated variable were process temperature and pressure. From this research it was obtained that equilibrium constant for MgCl 2 and Mg were expressed in the equation K M g C l 2 = 0.9011 P 1 .3779 1.06552 T and K M g = 6.0115P + 1.35256T - 6.93912
Giussi, Juan M; Gastaca, Belen; Albesa, Alberto; Cortizo, M Susana; Allegretti, Patricia E
2011-02-01
The study of tautomerics equilibria is really important because the reactivity of each compound with tautomeric capacity can be determined from the proportion of each tautomer. In the present work the tautomeric equilibria in some γ,δ-unsaturated β-hydroxynitriles and γ,δ-unsaturated β-ketonitriles were studied. The first family of compounds presents two possible theoretical tautomers, nitrile and ketenimine, while the second one presents four possible theoretical tautomers, keto-nitrile, enol (E and Z)-nitrile and keto-ketenimine. The equilibrium in gas phase was studied by gas chromatography-mass spectrometry (GC-MS). Tautomerization enthalpies were calculated by this methodology, and results were compared with those obtained by density functional theory (DFT) calculations, observing a good agreement between them. Nitrile tautomers were favored within the first family of compounds, while keto-nitrile tautomers were favored in the second family. Copyright Â© 2010 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Tsivintzelis, Ioannis; Ali, Shahid; Kontogeorgis, Georgios
2014-01-01
density data for both CO2 and CO2–water and for vapor–liquid equilibrium for mixtures of CO2 with various compounds present in transport systems. In all of these cases we consider various possibilities for modeling CO2 (inert, self-associating using two-, three-, and four sites) and the possibility......The CPA (cubic-plus-association) equation of state is applied in this work to a wide range of systems of relevance to CO2 transport. Both phase equilibria and densities over extensive temperature and pressure ranges are considered. More specifically in this study we first evaluate CPA against......” for applying CPA to acid gas mixtures. The overall conclusion is that CPA performs satisfactorily; the model in most cases correlates well binary data and predicts with good accuracy multicomponent vapor–liquid equilibria. Among the various approaches investigated, the best ones are when cross association...
Blasco, Mónica; Gimeno, María J; Auqué, Luis F
2018-02-15
Geothermometrical calculations in low-medium temperature geothermal systems hosted in carbonate-evaporitic rocks are complicated because 1) some of the classical chemical geothermometers are, usually, inadequate (since they were developed for higher temperature systems with different mineral-water equilibria at depth) and 2) the chemical geothermometers calibrated for these systems (based on the Ca and Mg or SO 4 and F contents) are not free of problems either. The case study of the Arnedillo thermal system, a carbonate-evaporitic system of low temperature, will be used to deal with these problems through the combination of several geothermometrical techniques (chemical and isotopic geothermometers and geochemical modelling). The reservoir temperature of the Arnedillo geothermal system has been established to be in the range of 87±13°C being the waters in equilibrium with respect to calcite, dolomite, anhydrite, quartz, albite, K-feldspar and other aluminosilicates. Anhydrite and quartz equilibria are highly reliable to stablish the reservoir temperature. Additionally, the anhydrite equilibrium explains the coherent results obtained with the δ 18 O anhydrite - water geothermometer. The equilibrium with respect to feldspars and other aluminosilicates is unusual in carbonate-evaporitic systems and it is probably related to the presence of detrital material in the aquifer. The identification of the expected equilibria with calcite and dolomite presents an interesting problem associated to dolomite. Variable order degrees of dolomite can be found in natural systems and this fact affects the associated equilibrium temperature in the geothermometrical modelling and also the results from the Ca-Mg geothermometer. To avoid this uncertainty, the order degree of the dolomite present in the Arnedillo reservoir has been determined and the results indicate 18.4% of ordered dolomite and 81.6% of disordered dolomite. Overall, the results suggest that this multi
Nitroxides as redox probes of melanins: dark-induced and photoinduced changes in redox equilibria
International Nuclear Information System (INIS)
Sarna, T.; Korytowski, W.; Sealy, R.C.
1985-01-01
The interaction of nitroxide free radicals and their reduced products (hydroxylamines) with synthetic and natural melanins has been studied. Electron spin resonance spectroscopy was used to measure changes in radical concentration in the dark and during irradiation with visible or uv light. Some reduction of nitroxide occurs in the dark, and is reversible: the nitroxide can be completely regenerated by the one-electron oxidant ferricyanide. The kinetics of the process depend strongly on radical charge and pH. For positively charged nitroxides the rate is much faster than for either neutral or anionic radicals. At pH 10 the rate is about 20 times faster than at pH 5. Oxidation of hydroxylamine also can occur so that a redox equilibrium is established. The equilibrium constant has been estimated for the reaction between a nitroxide and melanin from autoxidation of 3,4-dihydroxyphenylalanine. Results are also dependent upon the type of melanin used and chemical modification (oxidation or reduction) of the melanin. Redox equilibria are altered during irradiation with either visible or uv light. Rapid oxidation of hydroxylamine to nitroxide is apparent, together with a slower reduction of nitroxide. Action spectra for these processes are related to those for melanin radical production and oxygen consumption in nitroxide-free melanin systems. Reduction of nitroxide is inhibited by oxygen, suggesting a competition between nitroxide and oxygen for photoinduced reducing equivalents
Computation of thermodynamic equilibria of nuclear materials in multi-physics codes
International Nuclear Information System (INIS)
Piro, M.H.; Lewis, B.J.; Thompson, W.T.; Simunovic, S.; Besmann, T.M.
2011-01-01
A new equilibrium thermodynamic solver is being developed with the primary impetus of direct integration into nuclear fuel performance and safety codes to provide improved predictions of fuel behavior. This solver is intended to provide boundary conditions and material properties for continuum transport calculations. There are several legitimate concerns with the use of existing commercial thermodynamic codes: 1) licensing entanglements associated with code distribution, 2) computational performance, and 3) limited capabilities of handling large multi-component systems of interest to the nuclear industry. The development of this solver is specifically aimed at addressing these concerns. In support of this goal, a new numerical algorithm for computing chemical equilibria is presented which is not based on the traditional steepest descent method or 'Gibbs energy minimization' technique. This new approach exploits fundamental principles of equilibrium thermodynamics, which simplifies the optimization equations. The chemical potentials of all species and phases in the system are constrained by the system chemical potentials, and the objective is to minimize the residuals of the mass balance equations. Several numerical advantages are achieved through this simplification, as described in this paper. (author)
International Nuclear Information System (INIS)
Zheng, Shaohua; Cheng, Hongye; Chen, Lifang; Qi, Zhiwen
2016-01-01
Highlights: • Lactate esters were studied as solvent to remove butanol from aqueous media. • (Liquid + liquid) equilibrium data were measured at T = 298.15 K and 1 atm. • Selectivity and 1-butanol partition coefficient were calculated. • COSMO-based study of separation efficiency on solvent structure was conducted. - Abstract: As bio-based solvents, lactate esters can be used as extractant for removing 1-butanol from the aqueous fermentation broths. In order to evaluate the separation efficiency of butyl lactate and 2-ethylhexyl lactate for the extraction of 1-butanol from its mixture with water, the (liquid + liquid) equilibrium for the ternary systems {water (1) + 1-butanol (2) + lactate ester (3)} were measured at T = 298.15 K. The 1-butanol partition coefficient varied in the range of 4.46 to 10.29, and the solvent selectivity within 32.12 to 108.18. For the separation of low-concentration butanol from fermentation broths, butyl lactate exhibits higher partition coefficient and lower selectivity than 2-ethylhexyl lactate. The NRTL model was employed to correlate the experimental data, and the COSMO-RS theory was utilized to predict the (liquid + liquid) equilibria and to analyze the influence of lactate esters on extraction efficiency.
Numerical investigation of three-dimensional single-species plasma equilibria on magnetic surfaces
International Nuclear Information System (INIS)
Lefrancois, Remi G.; Pedersen, Thomas Sunn; Boozer, Allen H.; Kremer, Jason P.
2005-01-01
Presented for the first time are numerical solutions to the three-dimensional nonlinear equilibrium equation for single-species plasmas confined on magnetic surfaces and surrounded by an equipotential boundary. The major-radial shift of such plasmas is found to be outward, qualitatively similar to the Shafranov shift of quasineutral plasmas confined on magnetic surfaces. However, this is the opposite of what occurs in the pure toroidal field equilibria of non-neutral plasmas (i.e., in the absence of magnetic surfaces). The effect of varying the number of Debye lengths in the plasma for the three-dimensional (3D) model is in agreement with previous 2D calculations: the potential varies significantly on magnetic surfaces for plasmas with few Debye lengths (a d ), and tends to be constant on surfaces when many Debye lengths are present (a > or approx. 10λ d ). For the case of a conducting boundary that does not conform to the outer magnetic surface, the plasma is shifted towards the conductor and the potential varies significantly on magnetic surfaces near the plasma edge. Debye shielding effects are clearly demonstrated when a nonuniform bias is applied to the boundary. Computed equilibrium profiles are presented for the Columbia Non-Neutral Torus [T. S. Pedersen, A. H. Boozer, J. P. Kermer, R. Lefrancois, F. Dahlgren, N. Pomphrey, W. Reiersen, and W. Dorland, Fusion Sci. Technol. 46, 200 (2004)], a stellarator designed to confine non-neutral plasmas
Shrinking droplets in electrospray ionization and their influence on chemical equilibria.
Wortmann, Arno; Kistler-Momotova, Anna; Zenobi, Renato; Heine, Martin C; Wilhelm, Oliver; Pratsinis, Sotiris E
2007-03-01
We investigated how chemical equilibria are affected by the electrospray process, using simultaneous in situ measurements by laser-induced fluorescence (LIF) and phase Doppler anemometry (PDA). The motivation for this study was the increasing number of publications in which electrospray ionization mass spectrometry is used for binding constant determination. The PDA was used to monitor droplet size and velocity, whereas LIF was used to monitor fluorescent analytes within the electrospray droplets. Using acetonitrile as solvent, we found an average initial droplet diameter of 10 microm in the electrospray. The PDA allowed us to follow the evolution of these droplets down to a size of 1 microm. Rhodamine B-sulfonylchloride was used as a fluorescent analyte within the electrospray. By spatially resolved LIF it was possible to probe the dimerization equilibrium of this dye. Measurements at different spray positions showed no influence of the decreasing droplet size on the monomer-dimer equilibrium. However, with the fluorescent dye pair DCM and oxazine 1 it was shown that a concentration increase does occur within electrosprayed droplets, using fluorescence resonance energy transfer as a probe for the average pair distance.
Donnet, Marcel; Bowen, Paul; Lemaître, Jacques
2009-12-15
Thermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann's approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thus possible equilibrium precipitation pathways can be evaluated by calculating the evolution of surface charge, particle size and/or interfacial energy during the ongoing reaction. The approach includes the use of the Kelvin's law to express the influence of particle size on the solubility constant of precipitates, the use of Nernst's law to calculate surface potentials from solubility calculations and relate this to experimentally measured zeta potentials. Calcium carbonate precipitation and zeta potential measurements of well characterised high purity calcite have been used as a model system to validate the calculated values. The clarification of the change in zeta potential on titration illustrates the power of this approach as a tool for reaction pathway prediction and hence knowledge based tailoring of precipitation reactions.
Solvent isotope effects on tautomerization equilibria of papain and model thiolamines
International Nuclear Information System (INIS)
Creighton, D.J.; Schamp, D.J.
1980-01-01
The state of ionization of the active site sulfhydryl group of papain at the pH-optimum of activity (pH approximately 6.5) remains a controversial issue. An alternative approach to the problem is reported here which utilizes the difference between the isotopic fractionation factor of the S-H bond (phi approximately equal to 0.4) and the N-H bond (phi = 0.97). In principle, the tautomerization equilibrium should be subject to an inverse solvent deuterium isotope effect in which the non-ionised form is more stable relative to the ionised form in D 2 O compared to H 2 O (K(H 2 O)/K(D 2 O) = phisub(SH)/phisub(MH) approximately equal to 0.4). This priniciple has been successfully tested on the tautomerization equilibria of cysteine and β-mercaptoethylamine from spectrophotometric titrations. To the extent that these simple thiolamines model the spectral properties of the tautomeric species envisioned in the active site of papain, the tautomerization equilibrium constant for papain is estimated (K(H 2 O) approximately equal to 2) from a comparison of the effect of solvent D 2 O on the mercaptide ion spectra of the thiolamines and the mercaptide ion-like difference absorption spectrum of papain. (Auth.)
Turbulent Equilibria for Charged Particles in Space
Yoon, Peter
2017-04-01
The solar wind electron distribution function is apparently composed of several components including non-thermal tail population. The electron distribution that contains energetic tail feature is well fitted with the kappa distribution function. The solar wind protons also possess quasi power-law tail distribution function that is well fitted with an inverse power law model. The present paper discusses the latest theoretical development regarding the dynamical steady-state solution of electrons and Langmuir turbulence that are in turbulent equilibrium. According to such a theory, the Maxwellian and kappa distribution functions for the electrons emerge as the only two possible solution that satisfy the steady-state weak turbulence plasma kinetic equation. For the proton inverse power-law tail problem, a similar turbulent equilibrium solution can be conceived of, but instead of high-frequency Langmuir fluctuation, the theory involves low-frequency kinetic Alfvenic turbulence. The steady-state solution of the self-consistent proton kinetic equation and wave kinetic equation for Alfvenic waves can be found in order to obtain a self-consistent solution for the inverse power law tail distribution function.
Excitation equilibria in plasmas; a classification
International Nuclear Information System (INIS)
Mullen, J.A.M. van der
1990-01-01
This review gives a classification of the excitation kinetics ruled by electrons in plasmas. It is a study on the atomic state distribution function (ASDF) and its relation with underlying processes, which, for the case of an electron excitation kinetics (EEK) plasma, is merely a competition between free and bound electrons, the same particles in different circumstances. In a quasi steady state the population density of an atomic state results from production-destruction balances in equilibrium. If all balances are proper, i.e., consist of each other's inverse processes, then the ASDF is described by the Boltzmann-Saha relation. In other cases the balance will be denoted as improper, the ASDF will deviate from the equilibrium shape, but reflecting the underlying improper balances, it may give information about the plasma. Four improper balances and their impact on the ASDF are dealt with. An important feature is that improper balances are associated with particle transport. Special attention is paid to the distribution function of the excitation saturation balance in which the overpopulated bound electrons are subjected to frequent interactions with free electrons and the energy distribution of the free electrons is taken over. This distribution, denoted as the bound Maxwell distribution, is experimentally found in several ionizing plasmas. Its recombining counterpart, the deexcitation saturation balance, creates under certain conditions inversion in the ASDF, the basis for the recombination laser. (orig.)
Equilibrium and non equilibrium in fragmentation
International Nuclear Information System (INIS)
Dorso, C.O.; Chernomoretz, A.; Lopez, J.A.
2001-01-01
Full text: In this communication we present recent results regarding the interplay of equilibrium and non equilibrium in the process of fragmentation of excited finite Lennard Jones drops. Because the general features of such a potential resemble the ones of the nuclear interaction (fact that is reinforced by the similarity between the EOS of both systems) these studies are not only relevant from a fundamental point of view but also shed light on the problem of nuclear multifragmentation. We focus on the microscopic analysis of the state of the fragmenting system at fragmentation time. We show that the Caloric Curve (i e. the functional relationship between the temperature of the system and the excitation energy) is of the type rise plateau with no vapor branch. The usual rise plateau rise pattern is only recovered when equilibrium is artificially imposed. This result puts a serious question on the validity of the freeze out hypothesis. This feature is independent of the dimensionality or excitation mechanism. Moreover we explore the behavior of magnitudes which can help us determine the degree of the assumed phase transition. It is found that no clear cut criteria is presently available. (Author)
Stochastic Equilibria under Imprecise Deviations in Terminal-Reward Concurrent Games
Directory of Open Access Journals (Sweden)
Patricia Bouyer
2016-09-01
Full Text Available We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward objectives, and their existence is undecidable with qualitative reachability objectives (and only three players. However, these results rely on the fact that the players can enforce infinite plays while trying to improve their payoffs. In this paper, we introduce a relaxed notion of equilibria, where deviations are imprecise. We prove that contrary to Nash equilibria, such (stationary equilibria always exist, and we develop a PSPACE algorithm to compute one.
Stability of equilibria for a two-phase osmosis model
Lippoth, F.; Prokert, G.
2012-01-01
For a two-phase moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove that the manifold of equilibria is locally exponentially attractive. Our method relies on maximal regularity results for parabolic systems with relaxation type
A Numerical Algorithm to find All Scalar Feedback Nash Equilibria
Engwerda, J.C.
2013-01-01
Abstract: In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Predicting phase equilibria in one-component systems
Korchuganova, M. R.; Esina, Z. N.
2015-07-01
It is shown that Simon equation coefficients for n-alkanes and n-alcohols can be modeled using critical and triple point parameters. Predictions of the phase liquid-vapor, solid-vapor, and liquid-solid equilibria in one-component systems are based on the Clausius-Clapeyron relation, Van der Waals and Simon equations, and the principle of thermodynamic similarity.
Field line diversion properties of finite β Helias equilibria
International Nuclear Information System (INIS)
Hayashi, T.; Schwenn, U.; Strumberger, E.
1992-03-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite β-equilibria. The results support a divertor concept which has been developed from the diversion properties of the corresponding vacuum field. Cross-field transport is simulated by a simplified scrape-off layer (SOL) model. (author)
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...... theory....
Close pairs of relative equilibria for identical point vortices
DEFF Research Database (Denmark)
Dirksen, Tobias; Aref, Hassan
2011-01-01
Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are fou...
Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit
DEFF Research Database (Denmark)
Hubacek, Pavel; Park, Sunoo
2014-01-01
In this work we apply methods from cryptography to enable mutually distrusting players to implement broad classes of mediated equilibria of strategic games without trusted mediation. Our implementation uses a pre-play 'cheap talk' phase, consisting of non- binding communication between players...
Chemical Principles Revisited: Chemical Equilibrium.
Mickey, Charles D.
1980-01-01
Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)
Equilibrium and non-equilibrium phenomena in arcs and torches
Mullen, van der J.J.A.M.
2000-01-01
A general treatment of non-equilibrium plasma aspects is obtained by relating transport fluxes to equilibrium restoring processes in so-called disturbed Bilateral Relations. The (non) equilibrium stage of a small microwave induced plasma serves as case study.
Finite element computation of plasma equilibria
International Nuclear Information System (INIS)
Rivier, M.
1977-01-01
The applicability of the finite element method is investigated for the numerical solution of the nonlinear Grad-Shafranov equation with free boundary for the flux function of a plasma at equilibrium. This method is based on the case of variational principles and finite dimensional subspaces whose elements are piecewise polynomial functions obtained by a Lagrange type interpolation procedure over a triangulation of the domain. Two cases of plasma pressure (exponential and quadratic including a vacuum region) were examined. In both cases the nonuniqueness of the solutions was shown in exhibiting a deeper solution in the case of exponential pressure function, and a non-constant solution for a quadratic pressure function. In order to get this ''other'' solution, two linearization methods were tested with two different constraints. Different cross sections are investigated
Nash Equilibria in Theory of Reasoned Action
Almeida, Leando; Cruz, José; Ferreira, Helena; Pinto, Alberto Adrego
2009-08-01
Game theory and Decision Theory have been applied to many different areas such as Physics, Economics, Biology, etc. In its application to Psychology, we introduce, in the literature, a Game Theoretical Model of Planned Behavior or Reasoned Action by establishing an analogy between two specific theories. In this study we take in account that individual decision-making is an outcome of a process where group decisions can determine individual probabilistic behavior. Using Game Theory concepts, we describe how intentions can be transformed in behavior and according to the Nash Equilibrium, this process will correspond to the best individual decision/response taking in account the collective response. This analysis can be extended to several examples based in the Game Theoretical Model of Planned Behavior or Reasoned Action.
Excitation equilibria in plasmas: a classification
International Nuclear Information System (INIS)
Mullen, J.-J.A.M. van der.
1986-01-01
In this thesis the author presents a classification of plasmas based on the atomic state distribution function. The study is based on the relation between the distribution function and the underlying processes and starts with the proper understanding of thermodynamic equilibrium (TE). Four types of proper balances are relevant: The 'Maxwell balance' of kinetic energy transfer, the 'Boltzmann balance' of excitation/deexcitation, the 'Saha balance' of ionization/recombination and the 'Planck balance' for interaction of atoms with radiation. Special attention is paid to the distribution function of the ionizing excitation saturation balance. The classification theory of the distribution functions in relation with underlying balances is supported by experimental evidence in an ionizing argon plasma. The AR I system provides a pertinent support of the theory. Experimental facts found in the AR II system can be interpreted in global terms. (Auth.)
Bilinear Relative Equilibria of Identical Point Vortices
DEFF Research Database (Denmark)
Aref, H.; Beelen, Peter; Brøns, Morten
2012-01-01
, obtained using Sturm’s comparison theorem, is that if p(z) satisfies the ODE for a given q(z) with its imaginary zeros symmetric relative to the x-axis, then it must have at least n−m+2 simple, real zeros. For m=2 this provides a complete characterization of all zeros, and we study this case in some detail....... In particular, we show that, given q(z)=z 2+η 2, where η is real, there is a unique p(z) of degree n, and a unique value of η 2=A n , such that the zeros of q(z) and p(z) form a relative equilibrium of n+2 point vortices. We show that $A_{n} \\approx\\frac{2}{3}n + \\frac{1}{2}$, as n→∞, where the coefficient of n...
One-Dimensional Vlasov-Maxwell Equilibrium for the Force-Free Harris Sheet
International Nuclear Information System (INIS)
Harrison, Michael G.; Neukirch, Thomas
2009-01-01
In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet
Magnetoacoustic heating and FCT-equilibria in the belt pinch
International Nuclear Information System (INIS)
Erckmann, V.
1983-02-01
In the HECTOR belt pinch of high β plasma is produced by magnetic compression in a Tokamak geometry. After compresseion the initial β value can be varied between 0.2 and 0.8. During 5 μs the plasma is further heated by a fast magnetoacoustic wave with a frequency near the first harmonic of the ion cyclotronfrequency. For the first time the β-value of a pinch plasma could be increased further from 0.34 after compression to 0.46 at the end of the rf-heating cycle. By proper selection of the final β-value the region for resonance absorption of the heating wave can be shifted. Strong heating (200 MW) has been observed in the cases, where the resonance region has been located in the center of the plasma. In deuterium discharges an increase in ion temperature is observed during the heating process, whereas the electrons are energetically decoupled, showing no temperature increase. Strong plasma losses are found in the 200 MW range after the rf-heating process. The dominant mechanisms are charge exchange collisions with neutral gas atoms. During rf-heating and the subsequent cooling phase the magnetic flux is frozen due to the high conductivity of the plasma. The observed equilibria could be identified as flux conserving Tokamak (FCT) equilibria. Based on a two-dimensional code the time-evolution of the equilibria has been calculated. The q-profiles are time-independent, with increasing β the magnetic axis of the plasma is shifted towards the outer boundary of the torus, and finally the linear relation between β and βsub(pol), which is characteristic for low-β-equilibria, is no longer valid. Thus for the first time the existence of FCT-equilibria at high β has been demonstrated experimentally together with a qualitative agreement with FCT-theory. (orig./AH) [de
Directory of Open Access Journals (Sweden)
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
DIAGNOSIS OF FINANCIAL EQUILIBRIUM
Directory of Open Access Journals (Sweden)
SUCIU GHEORGHE
2013-04-01
Full Text Available The analysis based on the balance sheet tries to identify the state of equilibrium (disequilibrium that exists in a company. The easiest way to determine the state of equilibrium is by looking at the balance sheet and at the information it offers. Because in the balance sheet there are elements that do not reflect their real value, the one established on the market, they must be readjusted, and those elements which are not related to the ordinary operating activities must be eliminated. The diagnosis of financial equilibrium takes into account 2 components: financing sources (ownership equity, loaned, temporarily attracted. An efficient financial equilibrium must respect 2 fundamental requirements: permanent sources represented by ownership equity and loans for more than 1 year should finance permanent needs, and temporary resources should finance the operating cycle.
Equilibrium statistical mechanics
Mayer, J E
1968-01-01
The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t
Computing Equilibrium Chemical Compositions
Mcbride, Bonnie J.; Gordon, Sanford
1995-01-01
Chemical Equilibrium With Transport Properties, 1993 (CET93) computer program provides data on chemical-equilibrium compositions. Aids calculation of thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93/PC is version of CET93 specifically designed to run within 640K memory limit of MS-DOS operating system. CET93/PC written in FORTRAN.
International Nuclear Information System (INIS)
Blawzdziewicz, J.; Wajnryb, E.
2005-01-01
Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-sphere suspension using a Monte-Carlo method to evaluate thermodynamic equations of state. Coexisting phases are determined for systems in constrained- and full-equilibrium states that correspond to different stages of film relaxation. We also evaluated the effective viscosity coefficients for two-dimensional compressional and shear flows of a film and the self and collective mobility coefficients of the stabilizing particles. The hydrodynamic calculations were performed using a multiple-reflection representation of Stokes flow between two free surfaces. In this approach, the particle-laden film is equivalent to a periodic system of spheres with a unit cell that is much smaller in the transverse direction than in the lateral direction. (author)
Electricity market equilibrium model with resource constraint and transmission congestion
Energy Technology Data Exchange (ETDEWEB)
Gao, F. [ABB, Inc., Santa Clara, CA 95050 (United States); Sheble, G.B. [Portland State University, Portland, OR 97207 (United States)
2010-01-15
Electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models and many efforts have been made on it before. However, most past research focused on a single-period, single-market model and did not address the fact that GENCOs hold a portfolio of assets in both electricity and fuel markets. This paper first identifies a proper SFE model, which can be applied to a multiple-period situation. Then the paper develops the equilibrium condition using discrete time optimal control considering fuel resource constraints. Finally, the paper discusses the issues of multiple equilibria caused by transmission network and shows that a transmission constrained equilibrium may exist, however the shadow price may not be zero. Additionally, an advantage from the proposed model for merchant transmission planning is discussed. (author)
Electricity market equilibrium model with resource constraint and transmission congestion
International Nuclear Information System (INIS)
Gao, F.; Sheble, G.B.
2010-01-01
Electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models and many efforts have been made on it before. However, most past research focused on a single-period, single-market model and did not address the fact that GENCOs hold a portfolio of assets in both electricity and fuel markets. This paper first identifies a proper SFE model, which can be applied to a multiple-period situation. Then the paper develops the equilibrium condition using discrete time optimal control considering fuel resource constraints. Finally, the paper discusses the issues of multiple equilibria caused by transmission network and shows that a transmission constrained equilibrium may exist, however the shadow price may not be zero. Additionally, an advantage from the proposed model for merchant transmission planning is discussed. (author)
Thermal equilibrium properties of an intense relativistic electron beam
International Nuclear Information System (INIS)
Davidson, R.C.; Uhm, H.S.
1979-01-01
The thermal equilibrium properties of an intense relativistic electron beam with distribution function f 0 /sub b/=Z -1 /sub b/exp[-(H-β/sub b/cP/sub z/-ω/sub b/P/sub theta/) /T] are investigated. This choice of f 0 /sub b/ allows for a mean azimuthal rotation of the beam electrons (when ω/sub b/not =0), and corresponds to an important generalization of the distribution function first analyzed by Bennett. Beam equilibrium properties, including axial velocity profile V 0 /sub z/b(r), azimuthal velocity profile V 0 /sub thetab/(r), beam temperature profile T 0 /sub b/(r), beam density profile n 0 /sub b/(r), and equilibrium self-field profiles, are calculated for a broad range of system parameters. For appropriate choice of beam rotation velocity ω/sub b/, it is found that radially confined equilibrium solutions [with n 0 /sub b/(r→infinity) =0] exist even in the absence of a partially neutralizing ion background that weakens the repulsive space-charge force. The necessary and sufficient conditions for radially confined equilibria are ω - /sub b/ + /sub b/ for 0 2 /sub b/p /ω 2 /sub b/c) (1-f-β 2 /sub b/) 2 /sub b/p/ω 2 /sub b/c) (1-f-β 2 /sub b/) <0
Separation processes, I: Azeotropic rectification
Directory of Open Access Journals (Sweden)
Milojević Svetomir
2005-01-01
Full Text Available In a series of two articles, the problems of azeotrope separation (part I and the design of separation units (part II were analyzed. The basic definition and equations of vapour-liquid equilibria for ideal and non-ideal systems, the importance of the activity coefficient calculation necessary for the analysis of non-ideal equilibrium systems, as well as theoretical aspects of azeotrope rectification and the determination of the optimal third component (modifier or azeotrope agent are presented in the first part.
Multi-equilibrium property of metabolic networks: SSI module
Directory of Open Access Journals (Sweden)
Chen Luonan
2011-06-01
Full Text Available Abstract Background Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. Results In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. Conclusions In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module.
International Nuclear Information System (INIS)
Saien, Javad; Fattahi, Mahdi; Mozafarvandi, Maryam
2014-01-01
Highlights: • Experimental LLE data for water + acetic acid + toluene + NaCl or KCl were reported. • The salting-out effect was detected; indicating the stronger effect of NaCl. • The electrolyte-NRTL model was adequately used to correlate the phase equilibria. • A good agreement was observed between calculated and experimental tie-lines. - Abstract: The presence of salts can significantly alter the (liquid + liquid) equilibrium and extraction process. In this work, a study was conducted on the (liquid + liquid) equilibria of (water + acetic acid + toluene + sodium chloride or potassium chloride) at temperatures (288.2, 298.2 and 313.2) K. This chemical system, irrespective of salt, is frequently used in (liquid + liquid) extraction investigations. The selected salt concentrations in initial aqueous solutions were (0.9 and 1.7) mol · L −1 . The results show that salting-out effect of the salts was significant, so that an enhancement in the acetic acid distribution coefficient was achieved within (15.6 to 66.8)% with NaCl and within (2.5 to 37.6)% with KCl. Meantime, high separation factors were found at low temperatures and low solute concentrations. The electrolyte-NRTL model was satisfactorily used to correlate the phase equilibria. In this regard for each salt, the temperature dependent binary interaction parameters between components were calculated. The predicted tie-line mole fractions give root-mean square deviation (RMSD) values of only 0.0038 and 0.0045 for the systems containing NaCl and KCl, respectively
Bifurcated equilibria in centrifugally confined plasma
International Nuclear Information System (INIS)
Shamim, I.; Teodorescu, C.; Guzdar, P. N.; Hassam, A. B.; Clary, R.; Ellis, R.; Lunsford, R.
2008-01-01
A bifurcation theory and associated computational model are developed to account for abrupt transitions observed recently on the Maryland Centrifugal eXperiment (MCX) [R. F. Ellis et al. Phys. Plasmas 8, 2057 (2001)], a supersonically rotating magnetized plasma that relies on centrifugal forces to prevent thermal expansion of plasma along the magnetic field. The observed transitions are from a well-confined, high-rotation state (HR-mode) to a lower-rotation, lesser-confined state (O-mode). A two-dimensional time-dependent magnetohydrodynamics code is used to simulate the dynamical equilibrium states of the MCX configuration. In addition to the expected viscous drag on the core plasma rotation, a momentum loss term is added that models the friction of plasma on the enhanced level of neutrals expected in the vicinity of the insulators at the throats of the magnetic mirror geometry. At small values of the external rotation drive, the plasma is not well-centrifugally confined and hence experiences the drag from near the insulators. Beyond a critical value of the external drive, the system makes an abrupt transition to a well-centrifugally confined state in which the plasma has pulled away from the end insulator plates; more effective centrifugal confinement lowers the plasma mass near the insulators allowing runaway increases in the rotation speed. The well-confined steady state is reached when the external drive is balanced by only the viscosity of the core plasma. A clear hysteresis phenomenon is shown.
On phase equilibria in duplex stainless steels
Energy Technology Data Exchange (ETDEWEB)
Wessman, S. [Swerea KIMAB AB, Stockholm (Sweden); Pettersson, R. [Outokumpu Stainless AB, Avesta Research Centre, Avesta (Sweden); Hertzman, S. [Outokumpu Stainless Research Foundation, Stockholm (Sweden)
2010-05-15
The equilibrium conditions of four duplex stainless steels; Fe-23Cr-4.5Ni-0.1N, Fe-22Cr-5.5Ni-3Mo-0.17N, Fe-25Cr-7Ni-4Mo-0.27N and Fe-25Cr-7Ni-4Mo-1W-1.5Cu-0.27N were studied in the temperature region from 700 to 1000 C. Phase compositions were determined with SEM EDS and the phase fractions using image analysis on backscattered SEM images. The results showed that below 1000 C the steels develop an inverse duplex structure with austenite and sigma phase, of which the former is the matrix phase. With decreasing temperature, the microstructure will be more and more complex and finely dispersed. The ferrite is, for the higher alloyed steels, only stable above 1000 C and at lower temperatures disappears in favour of intermetallic phases. The major intermetallic phase is sigma phase with small amounts of chi phase, the latter primarily in high Mo and W grades. Nitrides, not a focus in this investigation, were present as rounded particles and acicular precipitates at lower temperatures. The results were compared to theoretical predictions using the TCFE5 and TCFE6 databases. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Jiang, Lingxiang; Yu, Caifang; Deng, Manli; Jin, Changwen; Wang, Yilin; Yan, Yun; Huang, Jianbin
2010-02-18
Cationic surfactant/anionic surfactant/beta-CD ternary aqueous systems provide a platform for the coexistence of the host-guest (beta-CD/surfactant) equilibrium and the biased aggregation (monomeric/aggregated surfactants) equilibrium. We report here that the interplay between the two equilibria dominates the systems as follows. (1) The biased aggregation equilibrium imposes an apparent selectivity on the host-guest equilibrium, namely, beta-CD has to always selectively bind the major surfactant (molar fraction > 0.5) even if binding constants of beta-CD to the pair of surfactants are quite similar. (2) In return, the host-guest equilibrium amplifies the bias of the aggregation equilibrium, that is, the selective binding partly removes the major surfactant from the aggregates and leaves the aggregate composition approaching the electroneutral mixing stoichiometry. (3) This composition variation enhances electrostatic attractions between oppositely charged surfactant head groups, thus resulting in less-curved aggregates. In particular, the present apparent host-guest selectivity is of remarkably high values, and the selectivity stems from the bias of the aggregation equilibrium rather than the difference in binding constants. Moreover, beta-CD is defined as a "stoichiometry booster" for the whole class of cationic/anionic surfactant systems, which provides an additional degree of freedom to directly adjust aggregate compositions of the systems. The stoichiometry boosting of the compositions can in turn affect or even determine microstructures and macroproperties of the systems.
Ferraro, N. M.; Jardin, S. C.; Lao, L. L.; Shephard, M. S.; Zhang, F.
2016-05-01
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M., E-mail: nferraro@pppl.gov; Lao, L. L. [General Atomics, La Jolla, California 92186 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Shephard, M. S.; Zhang, F. [Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2016-05-15
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Factors effecting carbonate equilibria in natural waters
International Nuclear Information System (INIS)
Snellman, M.
1987-12-01
This study is related to preliminary stie evaluations to be carried out in 1987-1992 for spent nuclear fuel disposal in Finland. Near surface and shallow groundwaters are characterized by high concentration of calcium and bicarbonate due to dissolution of calcite. The input of carbon dioxide in the upper zone of the bedrock has a strong influence on the pH giving a pH around neutral. In deep groundwaters when the system is no longer open to the input of carbon dioxide the pH rises as the carbonate system is displaced towards the bicarbonate-carbonate site. In still deeper parts of the rock weathering of other minerals such as feldspars affects the chemistry raising the pH and resulting in saturation and precipitation of calcite. The more advanced these reactions become the higher is the pH and the lower is the carbonate content. The equilibrium concentrations of carbonate species are affected both by temperature and ionic strength of the waters, at high ionic strength especially the distribution between bicarbonate and carbonate ions is affected. The total concentration of carbonates in groundwaters is determined through complex interaction between calcite and carbonates in the water. In deep groundwaters which are closed for input of CO 2 the concentration is stated to be regulated by dissolution of calcium carbonate. In deep granitic groundwaters pH is stated to be buffered to 6.5 to 10, where a high pH would correspond to a low total carbonate concentration and often also a low calcium concentration and a low pH would correspond to high carbonae and calcium concentrations
Equilibrium: three-dimensional configurations
International Nuclear Information System (INIS)
Anon.
1987-01-01
This chapter considers toroidal MHD configurations that are inherently three-dimensional. The motivation for investigation such complicated equilibria is that they possess the potential for providing toroidal confinement without the need of a net toroidal current. This leads to a number of advantages with respect to fusion power generation. First, the attractive feature of steady-state operation becomes more feasible since such configurations no longer require a toroidal current transformer. Second, with zero net current, one potentially dangerous class of MHD instabilities, the current-driven kink modes, is eliminated. Finally, three-dimensional configurations possess nondegenerate flux surfaces even in the absence of plasma pressure and plasma current. Although there is an enormous range of possible three-dimensional equilibria, the configurations of interest are accurately described as axisymmetric tori with superimposed helical fields; furthermore, they possess no net toroidal current. Instead, two different and less obvious restoring forces are developed: the helical sideband force and the toroidal dipole current force. Each is discussed in detail in Chapter 7. A detailed discussion of the parallel current constraint, including its physical significance, is given in section 7.2. A general analysis of helical sideband equilibria, along with a detailed description of the Elmo bumpy torus, is presented in sections 7.3 and 7.4. A general description of toroidal dipole-current equilibria, including a detailed discussion of stellarators, heliotrons, and torsatrons, is given in sections 7.5 and 7.6
Eberl, Gérard
2016-08-01
The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.
Sloshing-ion equilibria in the TARA endplugs
International Nuclear Information System (INIS)
Hokin, S.; Kesner, J.
1983-11-01
We have employed a modified version of the LLNL Bounce-average Fokker-Planck code to model neutral beam-produced sloshing-ion equilibria in the TARA endplugs. The questions we have addressed concern the effect of deuterium beam operation as opposed to hydrogen operation, and the advantage of using full-energy beams rather than the usual three-component beams. We find that, for the expected base case TARA operating parameters, a 40% savings in required beam power is attained by using deuterium beams rather than hydrogen beams, and that the use of full-energy beams results in an additional 26% power savings for these parameters. For higher plasma temperatures the use of full-energy beams becomes significantly advantagous. We have also investigated the equilibria of two possible alternate mirror configurations for the TARA endplugs, believed to be more stable to trapped particle modes, and report those results here
Phase diagrams and heterogeneous equilibria a practical introduction
Predel, Bruno; Pool, Monte
2004-01-01
This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.
Kempisty, Pawel; Strąk, Paweł; Sakowski, Konrad; Kangawa, Yoshihiro; Krukowski, Stanisław
2017-11-08
Thermodynamic foundations of ab initio modeling of vapor-solid and vapor-surface equilibria are introduced. The chemical potential change is divided into enthalpy and entropy terms. The enthalpy path passes through vapor-solid transition at zero temperature. The entropy path avoids the singular point at zero temperature passing a solid-vapor transition under normal conditions, where evaporation entropy is employed. In addition, the thermal changes are calculated. The chemical potential difference contribution of the following terms: vaporization enthalpy, vaporization entropy, the temperature-entropy related change, the thermal enthalpy change and mechanical pressure is obtained. The latter term is negligibly small for the pressure typical for epitaxy. The thermal enthalpy change is two orders smaller than the first three terms which have to be taken into account explicitly. The configurational vaporization entropy change is derived for adsorption processes. The same formulation is derived for vapor-surface equilibria using hydrogen at the GaN(0001) surface as an example. The critical factor is the dependence of the enthalpy of evaporation (desorption energy) on the pinning of the Fermi level bringing a drastic change of the value from 2.24 eV to -2.38 eV. In addition it is shown that entropic contributions considerable change the hydrogen equilibrium pressure over the GaN(0001) surface by several orders of magnitude. Thus a complete and exact formulation of vapor-solid and vapor-surface equilibria is presented.
Energy Technology Data Exchange (ETDEWEB)
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
Equilibrium shoreface profiles
DEFF Research Database (Denmark)
Aagaard, Troels; Hughes, Michael G
2017-01-01
Large-scale coastal behaviour models use the shoreface profile of equilibrium as a fundamental morphological unit that is translated in space to simulate coastal response to, for example, sea level oscillations and variability in sediment supply. Despite a longstanding focus on the shoreface...... profile and its relevance to predicting coastal response to changing environmental conditions, the processes and dynamics involved in shoreface equilibrium are still not fully understood. Here, we apply a process-based empirical sediment transport model, combined with morphodynamic principles to provide......; there is no tuning or calibration and computation times are short. It is therefore easily implemented with repeated iterations to manage uncertainty....
Czech Academy of Sciences Publication Activity Database
Sedláková, Zuzana; Malijevská, I.
2007-01-01
Roč. 261, 1-2 (2007) , s. 129-132 ISSN 0378-3812. [International Conference on Properties and Phase Equilibria for Product and Process Design PPEPPD 2007 /11./. Hersonissos, Crete, 20.05.2007-25.05.2007] Institutional research plan: CEZ:AV0Z40720504 Keywords : solid-liquid equilibrium * ternary system * solid adduct Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.506, year: 2007
Existence of equilibria in quantum Bertrand-Edgeworth duopoly game
Sekiguchi, Yohei; Sakahara, Kiri; Sato, Takashi
2012-12-01
Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.
(Liquid + liquid) equilibria of perfluorocarbons with fluorinated ionic liquids
International Nuclear Information System (INIS)
Martinho, S.; Araújo, J.M.M.; Rebelo, L.P.N.; Pereiro, A.B.; Marrucho, I.M.
2013-01-01
Highlights: • (Liquid + liquid) equilibria perfluorocarbons and fluorinated ionic liquids. • Non-Random Two Liquid model was successfully applied. • Thermodynamic functions that describe the solvation process were calculated. -- Abstract: In order to evaluate the feasibility of partially replace perfluorocarbons (PFCs) with fluorinated ionic liquids (FILs) in PFCs-in-water emulsions, usually used for biomedical purposes, herein the (liquid + liquid) phase equilibria of FILs containing fluorinated chains longer than four carbons with PFCs were carried out in a wide range of temperatures. With this goal in mind, two PFCs (perfluorooctane and perfluorodecalin) were selected and the (liquid + liquid) equilibria of the binary mixtures of these PFCs and FILs were studied at atmospheric pressure in a temperature range from T (293.15 to 343.15) K. For these studies, FILs containing ammonium, pyridinium and imidazolium cations and different anions with fluorocarbon alkyl chains between 4 and 8 were included. Additionally, Non-Random Two Liquid (NRTL) thermodynamic model was successfully applied to correlate the behaviour of the PFCs + FILs binary mixtures. Moreover, thermodynamic functions that describe the solvation process were calculated from the experimental data
Energy Technology Data Exchange (ETDEWEB)
Idriss, K A; Seleim, M M; Saleh, M S; Abu-Bakr, M S; Sedaira, Hassan
1988-11-01
The spectral absorption and acid-base characteristics of 1-amino-4-hydroxyanthraquinone (AMHA) were studied in water -ethanol media. The composition, molar absorptivities, equilibrium constants and stability constants of the chelates of this reagent with zirconium(IV) have been determined spectrophotometrically in 40% V/V ethanol at 20/sup 0/C and an ionic strength of 0.1 M (NaClO/sub 4/). Graphical logarithmic analysis of the absorbance graphs was used to demonstrate and characterise the complexation equilibria in solution. A simple, rapid, selective and sensitive method for the spectrophotometric determination of trace amounts of zirconium is proposed based on the formation of the Zr(AMHA)/sub 2/ complex at pH 3.5 (lambda/sub max/ = 600 nm, epsilon 1.621 x 10/sup 4/ l mol/sup -1/ cm/sup -1/). Interference caused by a number of ions was masked by the addition of cyanide ions.
Persat, Alexandre; Suss, Matthew E; Santiago, Juan G
2009-09-07
We present elements of electrolyte dynamics and electrochemistry relevant to microfluidic electrokinetics experiments. In Part I of this two-paper series, we presented a review and introduction to the fundamentals of acid-base chemistry. Here, we first summarize the coupling between acid-base equilibrium chemistry and electrophoretic mobilities of electrolytes, at both infinite and finite dilution. We then discuss the effects of electrode reactions on microfluidic electrokinetic experiments and derive a model for pH changes in microchip reservoirs during typical direct-current electrokinetic experiments. We present a model for the potential drop in typical microchip electrophoresis device. The latter includes finite element simulation to estimate the relative effects of channel and reservoir dimensions. Finally, we summarize effects of electrode and electrolyte characteristics on potential drop in microfluidic devices. As a whole, the discussions highlight the importance of the coupling between electromigration and electrophoresis, acid-base equilibria, and electrochemical reactions.
Thermodynamic Modeling of Multi-phase Solid–Liquid Equilibria in Industrial-Grade Oils and Fats
DEFF Research Database (Denmark)
Hjorth, Jeppe Lindegaard; Miller, Rasmus L.; Woodley, John M.
2015-01-01
Compositional thermodynamic phase separation is investigated for industrial-grade vegetable oils with complex compositions. Solid–liquid equilibria have been calculated by utilizing the Margules 2-suffix activity-coefficient model in combination with minimization of the Gibb’s free energy...... of the system. On the basis of quasi-equilibrium solid-fat content (SFC) measurements, a new approach to the estimation of the interaction parameters, needed for the activity-coefficient model, has been developed. The parameters are fitted by matching the SFC of two oils at various degrees of dilution...... and isothermal temperatures. Subsequently, the parameters are successfully validated against three oils, rich in asymmetric and symmetric triacylglycerols (TAG), respectively. The new approach developed is shown to be very flexible, allowing incorporation of additional TAG and polymorphic states. It thereby...
International Nuclear Information System (INIS)
Arce, Alberto; Francisco, Maria; Soto, Ana
2010-01-01
Suitability of a pyridinium ionic liquid as a solvent in desulfurization has been analyzed. (Liquid + liquid) equilibria for ternary systems composed by 1-hexyl-3,5-dimethyl pyridinium {bis[trifluoromethylsulfonyl]imide, thiophene, and three hydrocarbons representative of fuel (n-heptane, 2,2,4 trimethylpentane, and toluene) have been determined at T = 298.15 K and atmospheric pressure. High solubility of thiophene in the ionic liquid and also of toluene have been found, being this solvent practically immiscible with 2,2,4 trimethylpentane and heptane. Equilibrium data of these systems have been well correlated with UNIQUAC equations finding the highest deviations for the ternary system involving toluene. NRTL model drove to worse results being considered as not suitable model to correlate the experimental results.
Energy Technology Data Exchange (ETDEWEB)
Lee, Chul Soo; Lee, Se Il; Sim, Yeon Sik; Park, Sung Bin; Yang, Sung Oh; Park, Ji Yong [Korea University, Seoul (Korea, Republic of)
1995-08-01
In various partitioning processes, rare earth elements and actinide elements are separated from other elements in the first stage. They are then separated into rare earth groups and actinde groups. The first stage is accomplished by solvent extraction using DEHPA, by precipitation using oxalic= acid, or by cation exchange. The second stage is carried out by selective back-extraction or by selective elution using DTPA. In these processes the equilibria is governed by the concentrations of nitric acid, of solvents, and of precipitants among others. In this study various distribution coefficients in partitioning processes were experimentally determined. And thermodynamic models were proposed to calculate distribution coefficients with experimentally determined equilibrium constants. 32 refs., 11 tabs., 23 figs. (author)
Loomans, M. E.; Chi, D. Z.; Chua, S. J.
2004-10-01
Bulk-phase equilibria in Ni-rich/Si-rich alloys of the Ni-Pt-Si and Ni-Pd-Si systems were investigated. Results suggest that a bulk monosilicide solid solution, containing up to at least 11 at. pct Pt, exists in the Ni-Pt-Si system. Monosilicides containing more than 11 at. pct Pt were not examined. Results from both ternary systems point convincingly to the existence of a NiSi+Si↔NiSi2 eutectoid reaction near 700 °C in the Ni-Si binary system; data from the Ni-Pt-Si system, which yield the more accurate determination of the eutectoid temperature, place it at roughly 710 °C. The Pt and Pd concentrations of monosilicide in equilibrium with disilicide and Si were measured using energy-dispersive spectrometry (EDS) and were found to increase with temperature.
The Pierce diode with an external circuit. I. Oscillations about nonuniform equilibria
International Nuclear Information System (INIS)
Lawson, W.S.
1989-01-01
The nonuniform (nonlinear) equilibria of the classical (short circuit) Pierce diode and the extended (series RLC external circuit) Pierce diode are described, and the spectrum of oscillations (stable and unstable) about these equilibria are worked out. It is found that only the external capacitance alters the equilibria, though all elements alter the spectrum. In particular, the introduction of an external capacitor destabilizes some equilibria that are marginally stable without the capacitor. Computer simulations are performed to test the theoretical predictions for the case of an external capacitor only. It is found that most equilibria are correctly predicted by theory, but that the continuous set of equilibria of the classical Pierce diode at Pierce parameters (α=ω/sub pL//v 0 ) that are multiples of 2π are not observed. This appears to be a failure of the simulation method under the rather singular conditions rather than a failure of the theory
Microeconomics : Equilibrium and Efficiency
Ten Raa, T.
2013-01-01
Microeconomics: Equilibrium and Efficiency teaches how to apply microeconomic theory in an innovative, intuitive and concise way. Using real-world, empirical examples, this book not only covers the building blocks of the subject, but helps gain a broad understanding of microeconomic theory and
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness
Directory of Open Access Journals (Sweden)
Jieyu Ding
2014-01-01
Full Text Available Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.
International Nuclear Information System (INIS)
Munakata, Kenzo; Nishikawa, Masabumi; Fukumatsu, Teruki; Yamatsuki, Satoshi; Tanaka, Kenji
1999-01-01
The adsorption equilibria of Kr, Xe and N 2 , which are constituents of the off-gas from nuclear reprocessing processes, on representative adsorbents (Molecular Sieve 5A (MS5A) and activated charcoal) were studied. Adsorption experiments were conducted in the temperature range of 77 to 323 K using a packed bed column. The adsorption isotherms for the activated charcoal adsorbent were successfully correlated by the vacancy solution model. The adsorption isotherms for the MS5A adsorbent were properly correlated by the Langmuir model and the vacancy solution model. The adsorption experiments for the binary component systems (Kr-Xe, Kr-N 2 systems) were also performed, and the results suggest that the coexistence of Xe greatly inhibits the adsorption of Kr. The coexistence of large amounts of N 2 was also found to inhibit the adsorption of Kr. The experimental results for the adsorption equilibrium of binary component systems on the activated charcoal adsorbent were well reproduced by the vacancy solution model without parameter fitting. The binary adsorption equilibrium on the MS5A adsorbent is rather well predicted by the ideal adsorbed solution model without parameter fitting. The use of the vacancy solution model for this adsorption system requires the optimization of parameters, but the binary adsorption equilibrium is well reproduced with the optimized parameters. (author)
Comments on equilibrium, transient equilibrium, and secular equilibrium in serial radioactive decay
International Nuclear Information System (INIS)
Prince, J.R.
1979-01-01
Equations describing serial radioactive decay are reviewed along with published descriptions or transient and secular equilibrium. It is shown that terms describing equilibrium are not used in the same way by various authors. Specific definitions are proposed; they suggest that secular equilibrium is a subset of transient equilibrium
Investigations on application of multigrid method to MHD equilibrium analysis
International Nuclear Information System (INIS)
Ikuno, Soichiro
2000-01-01
The potentiality of application for Multi-grid method to MHD equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearization of the equation, the problem is solved by use of the iterative method. Although the Red-Black SOR method or Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. The Multi-grid method is compared with the SOR method for the Poisson Problem. The results of computations show that the CPU time required for the Multi-grid method is about 1000 times as small as that for the SOR method. (author)
Free-boundary equilibrium studies for the large helical device
International Nuclear Information System (INIS)
Gardner, H.J.; Ichiguchi, K.
1993-06-01
A free-boundary version of the VMEC three-dimensional equilibrium code, together with a code, DIAGNO, to determine the response to a set of magnetic diagnostic coils has been applied to the Large Helical Device. Two sequences of equilibria were considered: one where an external vertical field was used to keep the plasma centered and another where the outwardly shifting plasma was truncated by a limiter. The predictions of a simple cylindrical model have been verified for a diamagnetic loop. A set of simple response curves has been obtained which should be useful for the analysis and control of the finite plasma. The ideal Mercier criterion suggests that the centered plasma might be more stable. (author)
An Equilibrium Analysis of the Gender Wage Gap
DEFF Research Database (Denmark)
Frederiksen, Elisabeth Hermann
This paper develops a theory of the gender wage gap. In a general equilibrium model, spouses devide their labor between a formal sector and a home sector. Due to indivisibility effects, productivity of labor in the formal sector is negatively related to labor used in the home; at the same time...... labor inputs are complementary in home production. We show that initial beliefs about the gender wage gap are self-fulfilling, and a central result is multiplicity of equilibria. Spouses allocate their labor equally, if they expect to earn the same wage rates, which ex post reinforces equal wage rates......; whereas they allocate their labor differently, if they expect to earn different wage rates. The latter situation manifests itself in a gender wage gap. By use of numerical examples, we show that welfare is highest when spouses allocate labor equally. We relate this finding to policy recommendations...
Stability and attractive basins of multiple equilibria in delayed two-neuron networks
International Nuclear Information System (INIS)
Huang Yu-Jiao; Zhang Hua-Guang; Wang Zhan-Shan
2012-01-01
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied. Sufficient conditions are established for checking the existence of (2r + 1) 2 equilibria in delayed recurrent neural networks. Under these conditions, (r + 1) 2 equilibria are locally exponentially stable, and (2r + 1) 2 — (r + 1) 2 — r 2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results. (general)
The Pierce diode with an external circuit: II, Non-uniform equilibria
International Nuclear Information System (INIS)
Lawson, W.S.
1987-01-01
The non-uniform (non-linear) equilibria of the classical (short circuit) Pierce diode and the extended (series RLC external circuit) Pierce diode are described theoretically, and explored via computer simulation. It is found that most equilibria are correctly predicted by theory, but that the continuous set of equilibria of the classical Pierce diode at α = 2π are not observed. The stability characteristics of the non-uniform equilibria are also worked out, and are consistent with the simulations. 8 refs., 22 figs., 3 tabs
Survey of the calculation of phase equilibria with the aid of the UNIFAC-method
Energy Technology Data Exchange (ETDEWEB)
Gmehling, J.; Rasmussen, P.; Fredenslund, A.
1981-09-01
In the design of diffusional separation processes and for many other practical purposes one needs quantitative estimates of phase equilibrium compositions. These compositions can today be predicted with good results using modern, two-parameter models for the excess Gibbs energy. However, since the number of different multicomponent mixtures of interest in chemical technology is very large, it is in practise often not possible to find experimental data in the literature for all the possible binary combinations. In these cases it is necessary to use a predictive approach. Today, group-contribution methods such as ASOG and UNIFAC may be used with confidence to predict liquid phase excess Gibbs energies. In these methods, the mixture is assumed to consist not of molecules but of the functional groups which, when added form the parent molecules. This has the advantage that a large number of mixtures of interest in chemical technology can be described in terms of relatively few parameters characterizing the interactions between the groups. This review article demonstrates the application of the UNIFAC method to various practical problems within phase equilibria. The UNIFAC method applies to mixtures of nonelectrolytes in the temperature range of 275-425 K and at pressures up to 10 bar.
Phase equilibria and thermodynamic functions for Ag-Hg and Cu-Hg binary systems
Energy Technology Data Exchange (ETDEWEB)
Liu, Yajun, E-mail: yajunliu@gatech.edu [School of Materials and Energy, Guangdong University of Technology, Guangzhou, Guangdong 510006 (China); Wang, Guan [School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, Guangdong 510006 (China); Wang, Jiang [School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin, Guangxi 541004 (China); Chen, Yang [Mining, Metallurgy and Materials Research Department, General Research Institute for Nonferrous Metals, Beijing 100088 (China); Long, Zhaohui [School of Mechanical Engineering, Xiangtan University, Xiangtan, Hunan 411105 (China)
2012-11-10
Highlights: Black-Right-Pointing-Pointer The thermodynamic properties of Ag-Hg and Cu-Hg are explored in order to facilitate dental materials design. Black-Right-Pointing-Pointer A self-consistent set of thermodynamic parameters is obtained. Black-Right-Pointing-Pointer The experimental information can be well reproduced by the optimized thermodynamic data. - Abstract: In order to facilitate the computational design of new amalgams for novel dental alloys, the phase equilibria, phase diagrams and thermodynamic functions for Ag-Hg and Cu-Hg binary systems are explored in this work, based on the CALPHAD framework and experimental characterizations. The Gibbs free energies of the solution phases as well as the stoichiometric phases are calculated, with the aid of enthalpies of mixing, activities, enthalpies of formation, and phase equilibrium data. The thermodynamic descriptions provided in this work enable the stabilities of each phase at various temperatures and compositions to be well described, which contribute to the establishment of a general database to design novel metallic dental materials.
Theory and computation of general force balance in non-axisymmetric tokamak equilibria
Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan
2014-10-01
Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.
Phase equilibria and thermodynamic functions for Ag–Hg and Cu–Hg binary systems
International Nuclear Information System (INIS)
Liu, Yajun; Wang, Guan; Wang, Jiang; Chen, Yang; Long, Zhaohui
2012-01-01
Highlights: ► The thermodynamic properties of Ag–Hg and Cu–Hg are explored in order to facilitate dental materials design. ► A self-consistent set of thermodynamic parameters is obtained. ► The experimental information can be well reproduced by the optimized thermodynamic data. - Abstract: In order to facilitate the computational design of new amalgams for novel dental alloys, the phase equilibria, phase diagrams and thermodynamic functions for Ag–Hg and Cu–Hg binary systems are explored in this work, based on the CALPHAD framework and experimental characterizations. The Gibbs free energies of the solution phases as well as the stoichiometric phases are calculated, with the aid of enthalpies of mixing, activities, enthalpies of formation, and phase equilibrium data. The thermodynamic descriptions provided in this work enable the stabilities of each phase at various temperatures and compositions to be well described, which contribute to the establishment of a general database to design novel metallic dental materials.
DETERMINATION OF SOLID-LIQUID EQUILIBRIA DATA FOR MIXTURES OF HEAVY HYDROCARBONS IN A LIGHT SOLVENT
Energy Technology Data Exchange (ETDEWEB)
F.V. Hanson; J.V. Fletcher; Karthik R.
2003-06-01
A methodology was developed using an FT-IR spectroscopic technique to obtain solid-liquid equilibria (SLE) data for mixtures of heavy hydrocarbons in significantly lighter hydrocarbon diluents. SLE was examined in multiple Model Oils that were assembled to simulate waxes. The various Model oils were comprised of C-30 to C-44 hydrocarbons in decane. The FT-IR technique was used to identify the wax precipitation temperature (WPT). The DSC technique was also used in the identification of the onset of the two-phase equilibrium in this work. An additional Model oil made up of C-20 to C-30 hydrocarbons in decane was studied using the DSC experiment. The weight percent solid below the WPT was calculated using the FT-IR experimental results. The WPT and the weight percent solid below the WPT were predicted using an activity coefficient based thermodynamic model. The FT-IR spectroscopy method is found to successfully provide SLE data and also has several advantages over other laboratory-based methods.
Experimental investigation of the phase equilibria in the Co-Fe-Ti ternary system
Energy Technology Data Exchange (ETDEWEB)
Yuan, Chaohui; Chen, Chong; Peng, Yingbiao; Du, Yong; Li, Kun [Central South Univ., State Key of Powder Metallurgy, Changsha (China); Lu, Xingxu [Central South Univ., State Key of Powder Metallurgy, Changsha (China); Central South Univ., School of Materials Science and Engineering, Changsha (China)
2015-08-15
Phase equilibria in the Co-Fe-Ti ternary system were investigated by means of the equilibrated alloy method with X-ray powder diffraction and electron probe microanalysis. No ternary compounds were found. The experimental results indicated the existence of seven two-phase and one three-phase regions at 600 C, five two-phase and two three-phase regions at 800 C, and six two-phase and two three-phase regions at 950 C. The solubility of Co in TiFe{sub 2} was determined to be larger than 54 at.% at all investigated temperatures, and the solubilities of Fe in TiCo{sub 3} and Ti{sub 2}Co showed an appreciable increase with increasing temperature. The three-phase equilibrium in the Ti-rich corner at 800 C was revealed to be ((β-Ti) + Ti(Fe, Co) + Ti{sub 2}Co) rather than ((α-Ti) + Ti(Fe, Co) + Ti{sub 2}Co) reported in previous investigations. Based on the experimental data obtained in the present work, three isothermal sections at 600, 800 and 950 C were established.
The Zr-Ti-Cr system. Equilibria at 900 and 1100 C degrees
International Nuclear Information System (INIS)
Arico, Sergio F.; Gribaudo, Luis M.
2003-01-01
Main contributions to the knowledge of the ternary system Zr-Ti-Cr were published in the sixties. Stability domains of phases at temperatures between 500 and 1400 C degrees were there presented. Here, results related to the phase diagram at 900 and 1100 C degrees are informed. Three alloys with 40 at.% Cr and different Zr/Ti ratios and one more, richer in Cr, were elaborated. Specimens of the alloys were heat treated 1000 and 800 h at 900 and 1100 C degrees respectively. Phase characterizations were performed by optic metallography and X-ray diffraction analysis. Compositions were determined by microprobe. Alloys with 40 at.% Cr at both temperatures have biphasic equilibria between the intermetallic Laves phase AB 2 and the body-centered cubic solid solution containing principally zirconium and titanium. The Cr-rich alloy presents equilibrium of the AB 2 compound and the Cr-rich solid solution. Results of the present and previous works are used in order to propose new isothermal sections at 900 and 1100 C degrees. (author)
The calculation of phase equilibria of oxide core-concrete systems
International Nuclear Information System (INIS)
Ball, R.G.J.; Mignanelli, M.A.; Barry, T.I.; Gisby, J.A.
1993-01-01
Thermodynamic models have been developed to describe the phase equilibria of oxide solutions appropriate for the understanding of the chemical interactions between nuclear reactor core debris and concrete. For this purpose, the Gibbs energy of the liquid phase is described by the inclusion of associate species and nonideal interactions between the components and associate species. Assessments of the thermodynamic and phase equilibrium data for the subsystems of the CaO-Al 2 O 3 -SiO 2 -UO 2 -ZrO 2 system have been used to obtain a thermodynamic description of the crystalline and liquid phases in good agreement with published data. The data for the subsystems have then been combined, using well established principles, to predict the phase relationships in the ternary and quaternary sytsems and in the overall quinary system. The results show that he overall system cannot properly be treated as a pseudo-ideal liquid and solid solution, as used in some computer codes which attempt to model the physics and chemistry of core-concrete interactions. The limitations of the current model are discussed. (orig.)
Directory of Open Access Journals (Sweden)
A. V. Stepanov
2014-01-01
Full Text Available A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere.We consider the problem of transient stability analysis for a system of synchronous generators under the action of strong perturbations. The aim of our work is to develop methods to analyze a transient stability of the system of synchronous generators, which allow getting trustworthy results on reserve transient stability under different perturbations. For the analysis of transient stability, we use the direct Lyapunov method.One of the problems for this method application is to find the Lypunov function that well reflects the properties of a parallel system of synchronous generators. The most reliable results were obtained when the analysis of transient stability was performed with a Lyapunov function of energy type. Another problem for application of the direct Lyapunov method is to determine the critical value of the Lyapunov function, which requires finding the non-stable equilibria of the system. Determination of the non-stable equilibria requires studying the Lyapunov function in a multidimensional space in a neighborhood of a stable equilibrium for the post-breakdown system; this is a complicated non-linear problem.In the paper, we propose a method for determination of the non-stable equilibria on a multidimensional sphere. The method is based on a search of a minimum of the Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. Our method allows, comparing with the other, e.g., gradient methods, reliable finding a non-stable equilibrium and calculating the critical value. The reliability of our method is proved by numerical experiments. The developed methods and a program realized in a MATLAB package can be recommended for design of a post-breakdown control system of synchronous generators or as a
Existence and uniqueness of consistent conjectural variation equilibrium in electricity markets
International Nuclear Information System (INIS)
Liu, Youfei; Cai, Bin; Ni, Y.X.; Wu, Felix F.
2007-01-01
The game-theory based methods are widely applied to analyze the market equilibrium and to study the strategic behavior in the oligopolistic electricity markets. Recently, the conjecture variation approach, one of well-studied methods in game theory, is reported to model the strategic behavior in deregulated electricity markets. Unfortunately, the conjecture variation models have been criticized for the drawback of logical inconsistence and possibility of abundant equilibria. Aiming for this, this paper investigates the existence and uniqueness of consistent conjectural variation equilibrium in electricity markets. With several good characteristics of the electricity market and with an infinite horizon optimization model, it is shown that the consistent conjecture variation will satisfy a set of coupled nonlinear equations and there will be only one equilibrium. This result can provide the fundamentals for further applications of the conjecture variation approach. (author)
Isothermal phase equilibria for the (HFC-32 + HFC-134a) mixed-gas hydrate system
International Nuclear Information System (INIS)
Miyauchi, Hiroshi; Yasuda, Kenjiro; Matsumoto, Yuuki; Hashimoto, Shunsuke; Sugahara, Takeshi; Ohgaki, Kazunari
2012-01-01
Highlights: ► Structural phase transition results in the heterogeneous azeotropic-like behaviour. ► HFC-134a molecules, in spite of an s-II former, occupy the large cages of s-I. ► Negative azeotropic-like behaviour becomes more remarkable at higher temperatures. - Abstract: Isothermal phase equilibria (pressure-composition relations in hydrate, gas, and aqueous phases) in the {difluoromethane (HFC-32) + 1,1,1,2-tetrafluoroethane (HFC-134a)} mixed-gas hydrate system were measured at the temperatures 274.15 K, 279.15 K, and 283.15 K. The heterogeneous azeotropic-like behaviour derived from the structural phase transition of (HFC-32 + HFC-134a) mixed-gas hydrates appears over the whole temperature range of the present study. In addition to the heterogeneous azeotropic-like behaviour, the isothermal phase equilibrium curves of the (HFC-32 + HFC-134a) mixed-gas hydrate system exhibit the negative homogeneous azeotropic-like behaviour at temperatures 279.15 K and 283.15 K. The negative azeotropic-like behaviour, which becomes more remarkable at higher temperatures, results in the lower equilibrium pressure of (HFC-32 + HFC-134a) mixed-gas hydrates than those of both simple HFC-32 and HFC-134a hydrates. Although the HFC-134a molecule forms the simple structure-II hydrate at the temperatures, the present findings reveal that HFC-134a molecules occupy a part of the large cages of the structure-I mixed-gas hydrate.
Liu, Qinli; Ding, Xin; Du, Bowen; Fang, Tao
2017-11-02
Supercritical water oxidation (SCWO), as a novel and efficient technology, has been applied to wastewater treatment processes. The use of phase equilibrium data to optimize process parameters can offer a theoretical guidance for designing SCWO processes and reducing the equipment and operating costs. In this work, high-pressure phase equilibrium data for aromatic compounds+water systems and inorganic compounds+water systems are given. Moreover, thermodynamic models, equations of state (EOS) and empirical and semi-empirical approaches are summarized and evaluated. This paper also lists the existing problems of multi-phase equilibria and solubility studies on aromatic compounds and inorganic compounds in sub- and supercritical water.
Hidayat, Taufiq; Fallah-Mehrjardi, Ata; Hayes, Peter C.; Jak, Evgueni
2018-04-01
New experimental data were obtained on the gas/slag/matte/spinel equilibria in the Cu-Fe-O-S-Si system at 1473 K (1200 °C) and P(SO2) = 0.25 atm covering Cu concentrations in matte between 42 and 78 wt pct Cu. Accurate measurements were obtained using high-temperature equilibration and the rapid quenching technique, followed by electron-probe X-ray microanalysis of equilibrium phase compositions. The use of spinel substrates made to support the samples ensures equilibrium with this primary phase solid, eliminates crucible contamination, and facilitates direct gas-condensed phase equilibrium and high quenching rates. Particular attention was given to the confirmation of the achievement of equilibrium. The results quantify the relationship between Cu in matte and oxygen partial pressure, sulfur in matte, oxygen in matte, Fe/SiO2 at slag liquidus, sulfur in slag, and dissolved copper in slag.
Warm-fluid description of intense beam equilibrium and electrostatic stability properties
International Nuclear Information System (INIS)
Lund, S.M.; Davidson, R.C.
1998-01-01
A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij endash Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with ∂/∂θ=0 and ∂/∂z=0 about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be identical to the eigenfunction derived in a full kinetic treatment. However, in contrast to the kinetic treatment, the warm-fluid model predicts stable oscillations. None of the instabilities that are present in a kinetic description are obtained in the fluid model. A careful comparison of the mode oscillation frequencies associated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which may have general applicability. copyright 1998 American Institute of Physics
Equilibrium and pre-equilibrium emissions in proton-induced ...
Indian Academy of Sciences (India)
necessary for the domain of fission-reactor technology for the calculation of nuclear transmutation ... tions occur in three stages: INC, pre-equilibrium and equilibrium (or compound. 344. Pramana ... In the evaporation phase of the reaction, the.
Gated equilibrium bloodpool scintigraphy
International Nuclear Information System (INIS)
Reinders Folmer, S.C.C.
1981-01-01
This thesis deals with the clinical applications of gated equilibrium bloodpool scintigraphy, performed with either a gamma camera or a portable detector system, the nuclear stethoscope. The main goal has been to define the value and limitations of noninvasive measurements of left ventricular ejection fraction as a parameter of cardiac performance in various disease states, both for diagnostic purposes as well as during follow-up after medical or surgical intervention. Secondly, it was attempted to extend the use of the equilibrium bloodpool techniques beyond the calculation of ejection fraction alone by considering the feasibility to determine ventricular volumes and by including the possibility of quantifying valvular regurgitation. In both cases, it has been tried to broaden the perspective of the observations by comparing them with results of other, invasive and non-invasive, procedures, in particular cardiac catheterization, M-mode echocardiography and myocardial perfusion scintigraphy. (Auth.)
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Equilibrium statistical mechanics
Jackson, E Atlee
2000-01-01
Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t
DEFF Research Database (Denmark)
Bollerslev, Tim; Sizova, Natalia; Tauchen, George
Stock market volatility clusters in time, carries a risk premium, is fractionally inte- grated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast i......, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes....
Molecular equilibrium with condensation
International Nuclear Information System (INIS)
Sharp, C.M.; Huebner, W.F.
1990-01-01
Minimization of the Gibbs energy of formation for species of chemical elements and compounds in their gas and condensed phases determines their relative abundances in a mixture in chemical equilibrium. The procedure is more general and more powerful than previous abundance determinations in multiphase astrophysical mixtures. Some results for astrophysical equations of state are presented, and the effects of condensation on opacity are briefly indicated. 18 refs
Equilibrium calculations, ch. 6
International Nuclear Information System (INIS)
Deursen, A.P.J. van
1976-01-01
A calculation is presented of dimer intensities obtained in supersonic expansions. There are two possible limiting considerations; the dimers observed are already present in the source, in thermodynamic equilibrium, and are accelerated in the expansion. Destruction during acceleration is neglected, as are processes leading to newly formed dimers. On the other hand one can apply a kinetic approach, where formation and destruction processes are followed throughout the expansion. The difficulty of this approach stems from the fact that the density, temperature and rate constants have to be known at all distances from the nozzle. The simple point of view has been adopted and the measured dimer intensities are compared with the equilibrium concentration in the source. The comparison is performed under the assumption that the detection efficiency for dimers is twice the detection efficiency for monomers. The experimental evidence against the simple point of view that the dimers of the onset region are formed in the source already, under equilibrium conditions, is discussed. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Ikari, A.; Hatate, Y.; Uemura, Y. [Kagoshima University, Kagoshima (Japan). Faculty of Engineering
1997-01-10
Vapor-liquid equilibria of a water-methanol-ethanol system containing a minute amount of furfural were measured at atmospheric pressure by use of an Othmer-type still. The experimental results are represented by four triangular diagrams against the liquid compositions of the major components (water, methanol and ethanol), in which three diagrams show the vapor composition of the major components, respectively, and one diagram shows the equilibrium ratio of the trace component (furfural). The curved surface of the equilibrium ratio of the trace component exhibits a gentle downward slope in most areas, but shows a half-saddle face in the neighborhood of the water-ethanol side. 4 refs., 10 figs., 3 tabs.
Equilibrium Reconstruction in EAST Tokamak
International Nuclear Information System (INIS)
Qian Jinping; Wan Baonian; Shen Biao; Sun Youwen; Liu Dongmei; Xiao Bingjia; Ren Qilong; Gong Xianzu; Li Jiangang; Lao, L. L.; Sabbagh, S. A.
2009-01-01
Reconstruction of experimental axisymmetric equilibria is an important part of tokamak data analysis. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. Benchmarking and testing calculations are performed to evaluate and validate this algorithm. Two cases for circular and non-circular plasma discharges are presented. Fourier expansion used to fit the eddy current is a robust method and the real time EFIT can be introduced to the plasma control system in the coming campaign. (magnetically confined plasma)
Noncompact Equilibrium Points and Applications
Directory of Open Access Journals (Sweden)
Zahra Al-Rumaih
2012-01-01
Full Text Available We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.
Equilibrium thermodynamics - Callen's postulational approach
Jongschaap, R.J.J.; Öttinger, Hans Christian
2001-01-01
In order to provide the background for nonequilibrium thermodynamics, we outline the fundamentals of equilibrium thermodynamics. Equilibrium thermodynamics must not only be obtained as a special case of any acceptable nonequilibrium generalization but, through its shining example, it also elucidates
MHD equilibrium with toroidal rotation
International Nuclear Information System (INIS)
Li, J.
1987-03-01
The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)
International Nuclear Information System (INIS)
Meisel, D.; Czapski, G.
1976-01-01
The pulse radiolysis technique is utilized for measurements of the equilibrium constants for electron transfer between the durosemiquinone radical anion and oxygen, menadione and indigo disulfonate. These equilibrium constants are in turn used for calculations of one-electron redox potentials for these systems. Each of these equilibrium constants was determined experimentally and independently and found to be self consistent. Only for the reactions of the semiquinones with oxygen could the electron transfer reaction be followed directly. For the reactions between the various quinone/semiquinone systems substantial indirect evidence is presented that these equilibria are achieved rapidly. In those cases equilibrium constants were determined from studies of the effect of quinone concentrations on the relative yields of the semiquinones. A method for distinguishing between kinetic competition and equilibrium is outlined and its usefulness is emphasized. The DQ/DQ - (DQ = duroquinone) and IDS/IDS - (IDS = indigo disulfonate) systems were employed as reference couples as the redox potentials for those systems are either available in the literature (IDS/IDS - ) or may be calculated from available data (DQ/DQ - ). Taking E 7 1 , the redox potential for the first one-electron reduction step at pH 7, of DQ/DQ - as -0.235 volts or of IDS/IDS - as -0.125 volts, both yield E 7 1 = -0.325 V for the O 2 /O 2 - system (1 atm O 2 ) and E 7 1 = -0.20 for the menadione system
Phase equilibria constraints on the chemical and physical evolution of the campanian ignimbrite
Fowler, S.J.; Spera, F.J.; Bohrson, W.A.; Belkin, H.E.; de Vivo, B.
2007-01-01
The Campanian Ignimbrite is a > 200 km3 trachyte-phonolite pyroclastic deposit that erupted at 39.3 ?? 0.1 ka within the Campi Flegrei west of Naples, Italy. Here we test the hypothesis that Campanian Ignimbrite magma was derived by isobaric crystal fractionation of a parental basaltic trachyandesitic melt that reacted and came into local equilibrium with small amounts (5-10 wt%) of crustal rock (skarns and foid-syenites) during crystallization. Comparison of observed crystal and magma compositions with results of phase equilibria assimilation-fractionation simulations (MELTS) is generally very good. Oxygen fugacity was approximately buffered along QFM+1 (where QFM is the quartz-fayalite-magnetite buffer) during isobaric fractionation at 0.15 GPa (???6 km depth). The parental melt, reconstructed from melt inclusion and host clinopyroxene compositions, is found to be basaltic trachyandesite liquid (51.1 wt% SiO2, 9.3 wt% MgO, 3 wt% H2O). A significant feature of phase equilibria simulations is the existence of a pseudo-invariant temperature, ???883??C, at which the fraction of melt remaining in the system decreases abruptly from ???0.5 to point leads to abrupt changes in the composition, properties (density, dissolved water content), and physical state (viscosity, volume fraction fluid) of melt and magma. A dramatic decrease in melt viscosity (from 1700 Pa s to ???200 Pa s), coupled with a change in the volume fraction of water in magma (from ??? 0.1 to 0.8) and a dramatic decrease in melt and magma density acted as a destabilizing eruption trigger. Thermal models suggest a timescale of ??? 200 kyr from the beginning of fractionation until eruption, leading to an apparent rate of evolved magma generation of about 10-3 km3/year. In situ crystallization and crystal settling in density-stratified regions, as well as in convectively mixed, less evolved subjacent magma, operate rapidly enough to match this apparent volumetric rate of evolved magma production
Ideal MHD stability of high poloidal beta equilibria in TFTR
International Nuclear Information System (INIS)
Sabbagh, S.A.; Mauel, M.E.; Navratil, G.A.; Bell, M.G.; Budny, R.V.; Chance, M.S.; Fredrickson, E.D.; Jardin, S.C.; Manickam, J.; McCune, D.C.; McGuire, K.M.; Wieland, R.M.; Zarnstorff, M.C.; Phillips, M.W.; Hughes, M.H.; Kesner, J.
1991-01-01
Recent experiments in TFTR have expanded the operating space of the device to include plasmas with values of var-epsilon β p dia ≡ 2μ 0 var-epsilon perpendicular >/ p >> 2 as large as 1.6, and Troyon normalized diamagnetic beta β N dia ≡ β t perpendicular aB t /10 -8 I p as large as 4.7. At values of var-epsilon β p dia ≥ 1.3, a separatrix was observed to enter the vacuum vessel, producing a naturally diverted discharge. Plasmas with large values of var-epsilon β p dia were created with both the plasma current, I p , held constant and with I p decreased, or ramped down, before the start of neutral beam injection. A convenient characterization of the change in I p using experimental parameters can be defined by the ratio of I p before the ramp down, to I p during the neutral beam heating phase, F I p . The ideal MHD stability of these equilibria is investigated to determine their location in stability space, and to study the role of plasma current and pressure profile modification in the creation of these high var-epsilon β p and β N plasmas. The evolution of these plasmas is modelled from experimental data using the TRANSP code. Two-dimensional equilibria are computed from the TRANSP results and used as input to both high and low-n stability codes including PEST. The high var-epsilon β p equilibria, which generally have an oblate cross-sectional shape, are in the first stability region to high-n ballooning modes. At constant I p , these equilibria generally have maximum pressure gradients near the magnetic axis and are stable to n=1 modes without a stabilizing conducting wall. The effect of the current profile shape on the stability of low-n kink/ballooning modes and the requirements for these plasmas to access the second stability region are examined. 6 refs
Phase Equilibria Relationships of High-Tc Superconductors
International Nuclear Information System (INIS)
Wong-Ng, Winnie
2011-01-01
As an integral part of a R and D program partially supported by the Electricity Delivery and Energy Reliability Office of DOE, we have determined phase equilibria data and phase diagrams for the three generations of superconductor materials: 1st generation, (Bi,Pb)-Sr-Ca- Cu-O systems; 2nd generation, Ba-R-Cu-O systems (R=lanthanides and yttrium); and 3rd generation, MgB2 systems. Our studies involved bulk materials, single crystals and thin films. This report gives a summary of our accomplishments, a list of publications, and 15 selected journal publications.
The free energy of Maxwell-Vlasov equilibria
International Nuclear Information System (INIS)
Morrison, P.J.; Pfirsch, D.
1989-10-01
A previously derived expression for the energy of arbitrary perturbations about arbitrary Vlasov-Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov's equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed. 16 refs
Looking for multiple equilibria when geography matters : German city growth and the WWII shock
Bosker, Maarten; Brakman, Steven; Garretsen, Harry; Schramm, Marc
Based on the methodology of Davis and Weinstein, we look for multiple equilibria in German city growth. Bytaking the bombing of Germany during WWII as an example of a large, temporary shock, we analyze whether German city growth is characterized by multiple equilibria. In doing so, we allow for