Variational principles in chemical equilibria: Complex chemical systems with interacting subsystems
Zilbergleyt, B
2010-01-01
The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach the problem of complex equilibrium is solved by minimization of the system Gibbsâ free energy subject to logistic constraints. DTD demands any isolated system to comprise smaller subentities, which individual equilibria are based on the balance of internal and external thermodynamic forces, acting against them. The internal forces are equal to the subsystems thermodynamic affinities, while external forces originate from subsystems mutual interactions. Those interactions impose additional constraints on the mother system Gibbsâ free energy minimum. Basic expression of discrete thermodynamics, being multiplied by subsystems deviations from their âtrueâ thermodynamic equilibria, is naturally identical to dâAlembertâs principle. A thermodynamic ve...
Structures and Chemical Equilibria of Some N-Heterocycles Containing Amide Linkages
N. H. Abd El Moneim
2003-05-01
Full Text Available Structures and chemical equilibria of 5-carboxy-2-thiouracil (1, 5,6-diphenyl-3-hydroxy-1,2,4-triazine (2, 1-phenyl-3-methyl-5-pyrazolone (3 and 2-mercapto-4,6-dimethylpyrimidine hydrochloride (4 are reported. Their electronic transitions are assigned and pK values are evaluated and discussed.
van Bennekom, Joost G.; Winkelman, Jozef G. M.; Venderbosch, Robertus H.; Nieland, Sebastiaan D. G. B.; Heeres, Hero J.
2012-01-01
A solution method was developed to calculate the simultaneous phase and chemical equilibria in high-pressure methanol synthesis (P = 20 MPa, 463
Vapor-Liquid and Chemical Equilibria in the Ethanol + Acetic Acid System at 348.15 K.
Bernatová, Svatoslava; Aim, Karel; Wichterle, Ivan
2007-01-01
Roč. 52, 1 (2007) , s. 20-23. ISSN 0021-9568 R&D Projects: GA ČR(CZ) GA203/03/1588 Institutional research plan: CEZ:AV0Z40720504 Keywords : phase equilibria * chemical equilibria * esterification Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.729, year: 2007
Chemical exchange equilibria in isotope separation. Part I : Evaluation of separation factors
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.)
Thermodynamic modeling of chemical equilibria in metal extraction
Models of equilibrium extraction data are being developed for use in computer simulations of metal extraction processes. The correlations are based on chemical mass action principles in which the effects of metal complexation and aqueous phase activity coefficients are considered. Activity coefficients in mixed electrolyte solutions at high ionic strengths are calculated using methods available in the literature. This modeling approach is demonstrated for HNO3 extraction with both the PIREX and TRUEX solvents and for Am3+ extraction by octylphenyl-N,N-diisobutylcarbamoylmethylphosphine oxide, which is the primary extractant in the TRUEX solvent. 27 refs., 4 figs., 4 tabs
Described are some phase equilibria and chemical thermodynamics of systems relevant to the production and operation of the so-called ''advanced'' fast breeder reactor fuels. The systems discussed include UPu carbides, nitrides, oxycarbides and carbonitrides. Some examples of the application of these phase equilibria to the preparation, fabrication and behaviour of the materials in temperature gradients appropriate to reactor conditions are presented. Finally, aspects of the complex four and five component, U-C-O-N and U-Pu-C-O-N systems are discussed, a detailed knowledge of which is required for an analysis of advanced fuel behaviour
Chemical equilibria between C-S-H and ettringite, at 20 and 85 deg. C
Mixes of C-S-H and ettringite were synthesized in suspension systems and their equilibria were studied at 20 and 85 deg. C. Concentrations in solution (calcium, sulfate, aluminium) were measured and the mineralogical state of the systems was studied by means of X-ray diffraction. The equilibria between C-S-H and ettringite are described. The relative importance of sulfate bound to the C-S-H is evaluated. The kinetics of ettringite reprecipitation from a 'C-S-H-ettringite' system at 85 deg. C placed at 20 deg. C are also evaluated
Ranjbar, Faranak; Jalali, Mohsen
2015-11-01
In this study, the reclamation of a calcareous sodic soil with the exchangeable sodium percentage (ESP) value of 26.6% was investigated using the cheap and readily available chemical and organic materials including natural bentonite and zeolite saturated with calcium (Ca2+), waste calcite, three metal oxide nanoparticles functionalized with an acidic extract of potato residues, and potato residues. Chemical amendments were added to the soil at a rate of 2%, while potato residues were applied at the rates of 2 and 4% by weight. The ESP in the amended soils was reduced in the range of 0.9-4.9% compared to the control soil, and the smallest and the largest decline was respectively observed in treatments containing waste calcite and 4% of potato residues. Despite the reduction in ESP, the values of this parameter were not below 15% at the end of a 40-day incubation period. So, the effect of solutions of varying sodium adsorption ratio (SAR) values of 0, 5, 10, 20, 30, 40, and 50 on sodium (Na+) exchange equilibria was evaluated in batch systems. The empirical models (simple linear, Temkin, and Dubinin-Radushkevich) fitted well to experimental data. The relations of quantity to intensity (Q/I) revealed that the potential buffering capacity for Na+ (PBCNa) varied from 0.275 to 0.337 ((cmolc kg(-1)) (mmol L(-1))(-1/2)) in the control soil and amended soils. The relationship between exchangeable sodium ratio (ESR) and SAR was individually determined for the control soil and amended soils. The values of Gapon selectivity coefficient (KG) of Na+ differed from the value suggested by U.S. Salinity Laboratory (USSL). The PHREEQC, a geochemical computer program, was applied to simulate Na+ exchange isotherms by using the mechanistic cation exchange model (CEM) along with Gaines-Thomas selectivity coefficients. The simulation results indicated that Na+ exchange isotherms and Q/I and ESR-SAR relations were influenced by the type of counter anions. The values of K G increased in
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 th...
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 < 0.1. Crystallization at the pseudo-invariant 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
The value of the electrochemical technique Reverse Pulse Voltammetry (RPV) for the characterization of chemical equilibria in solution is theoretically investigated. For this, the RPV response of the square scheme is studied at spherical and disc electrodes of any size assuming that the chemical reactions are at equilibrium. When the effective diffusion coefficients of the oxidized and reduced species are the same, analytical solutions are reported for both electrode geometries. Otherwise, a rigorous analytical solution is derived for spherical electrodes whereas the case of microdiscs is addressed by numerical simulations. The theory for the square scheme enables the study of the RPV response in very different situations, including the cases where the electrochemical and/or chemical transformations alter significantly the species diffusivity such as in electron transfer processes in room temperature ionic liquids or in the association of the electroactive species with (bio) macromolecules and nanoparticles. It is found that, when medium-size (disc or spherical) microelectrodes are employed, the RPV method enables the simultaneous determination of the effective diffusion coefficients of the oxidized and reduced species as well as the apparent formal potential. These magnitudes make it possible a sound physicochemical characterization of the system
The use of available chemical equilibria software for the prediction of the performance of EKR
Villén Guzmán, María; Gómez-Lahoz, C.; García Rubio, Ana; Paz García, José Manuel; Vereda Alonso, Carlos; García Herruzo, Francisco; Rodríguez Maroto, José Miguel
2014-01-01
Risk assessment aims for the prediction of the mobility of contaminants, and these are usually based in lab essays together with mathematical modelling. Also the feasibility studies of most techniques, require similar tools. Frequently the lab characterization is based in the chemical fractionation of the contaminants based on their mobility under different chemical reagents. Probably the most frequent fractionation technique for heavy metal contaminated soils is the BCR [1]. The use of ch...
Thermodynamic modeling of chemical equilibria in liquid-liquid extraction of lutetium
The extraction equilibrium data of lutetium from sodium succinate solution with Aliquat 336 in benzene is systematically investigated. The aqueous phase metal complexation and polymerization in the organic phase are taken into account in obtaining extraction coefficients, stability constants, hydrolysis constants, solubility product, and extraction constants. A thermodynamic model of the above equilibrium extraction data is developed for use in computer simulation of the extraction process. The correlations are based on chemical mass action principles in which the metal complexation in the aqueous phase, polymerization in the organic phase, precipitation in the aqueous phase, and aqueous phase activity coefficients are considered. Extraction behavior of other lanthanides from a succinate medium is also discussed
Spalding, B P; Spalding, I R
2001-01-15
Strontium-90 is a major hazardous contaminant of radioactive wastewater and its processing sludges at many Department of Energy (DOE) facilities. In the past, such contaminated wastewater and sludge have been disposed in soil seepage pits, lagoons, or cribs often under highly perturbed alkaline conditions (pH > 12) where 90Sr solubility is low and its adsorption to surrounding soil is high. As natural weathering returns these soils to near-neutral or slightly acidic conditions, the adsorbed and precipitated calcium and magnesium phases, in which 90Sr is carried, change significantly in both nature and amounts. No comprehensive computational method has been formulated previously to quantitatively simulate the dynamics of 90Sr in the soil-groundwater environment under such dynamic and wide-ranging conditions. A computational code, the Hydrologic Utility Model for Demonstrating Integrated Nuclear Geochemical Environmental Responses (HUMDINGER), was composed to describe the changing equilibria of 90Sr in soil based on its causative chemical reactions including soil buffering, pH-dependent cation-exchange capacity, cation selectivity, and the precipitation/dissolution of calcium carbonate, calcium hydroxide, and magnesium hydroxide in response to leaching groundwater characteristics including pH, acid-neutralizing capacity, dissolved cations, and inorganic carbonate species. The code includes a simulation of one-dimensional transport of 90Sr through a soil column as a series of soil mixing cells where the equilibrium soluble output from one cell is applied to the next cell. Unamended soil leaching and highly alkaline soil treatments, including potassium hydroxide, sodium silicate, and sodium aluminate, were simulated and compared with experimental findings using large (10 kg) soil columns that were leached with 90Sr-contaminated groundwater after treatment. HUMDINGER's simulations were in good agreement with dynamic experimental observations of soil exchange capacity
Development of a self-standing numerical tool to solve chemical equilibria in nuclear materials
Many numerical codes are available to provide a prediction of nuclear fuel behaviour under normal and abnormal conditions. These codes typically require a method of capturing chemical phenomena and phase equilibrium in a system with many components. The integration of existing thermochemical software is complicated by the need to pass information through input and output operations between various programs since the source code is generally unavailable. Accordingly, fuel behaviour codes typically rely on empirical correlations to incorporate fuel physical chemistry knowledge for lack of a thermochemical solver that can be directly implemented within the code. The empirical correlations generally do not convey with high fidelity the original thermodynamic analysis. A numerical tool is being constructed to provide the equilibrium compositions of species and related thermochemical properties in multiphase-multicomponent systems through the process of Gibbs energy minimization. Standard Gibbs energies of formation for pure species are used along with models that describe the mixing of solute species dissolved in various non-ideal solution phases. Mass constraints are observed with the use of an internal linear equation solver employing Gaussian elimination. An impediment to many existing thermochemical codes is the inability of handling a sufficiency of components necessary to capture all of the fission products possibly produced. Furthermore, the ability to customize Gibbs energy formulations directly in the source code is a great convenience. For instance, it may be desirable to introduce thermodynamic models representing the non-ideal mixing of solute atoms using mathematical expressions that do not conform to the expectation of standard software. Thermodynamic models representing the non-stoichiometry of solid and liquid uranium dioxide can benefit from such sophisticated mathematical expressions. The programming is currently being applied to advance a
Kandori, Michihiro
1988-01-01
This paper provides a way to formulate a general equilibrium model with both infinite time horizon and continuous uncertainty by 2.space, and provides a si mple proof of the equiva-lence of equilibria in complete markets, inc omplete markets with sequential trading, and incomplete markets with one-shot trades in single consumer economies. The proof is general in the sense that it does not assume time-homogeneous structure nor smo othness of preferences. The result guarantees that one can avoi...
Dutrow, Barbara
2008-08-13
Our research evaluates the hypothesis that feedback amongst thermal-chemical-mechanical processes operative in fluid-rock systems alters the fluid flow dynamics of the system which, in turn, affects chemical transport and temporal and spatial scales of equilibria, thus impacting the resultant mineral textural development of rocks. Our methods include computational experimentation and detailed analyses of fluid-infiltrated rocks from well-characterized terranes. This work focuses on metamorphic rocks and hydrothermal systems where minerals and their textures are utilized to evaluate pressure (P), temperature (T), and time (t) paths in the evolution of mountain belts and ore deposits, and to interpret tectonic events and the timing of these events. Our work on coupled processes also extends to other areas where subsurface flow and transport in porous media have consequences such as oil and gas movement, geothermal system development, transport of contaminants, nuclear waste disposal, and other systems rich in fluid-rock reactions. Fluid-rock systems are widespread in the geologic record. Correctly deciphering the products resulting from such systems is important to interpreting a number of geologic phenomena. These systems are characterized by complex interactions involving time-dependent, non-linear processes in heterogeneous materials. While many of these interactions have been studied in isolation, they are more appropriately analyzed in the context of a system with feedback. When one process impacts another process, time and space scales as well as the overall outcome of the interaction can be dramatically altered. Our goals to test this hypothesis are: to develop and incorporate algorithms into our 3D heat and mass transport code to allow the effects of feedback to be investigated numerically, to analyze fluid infiltrated rocks from a variety of terranes at differing P-T conditions, to identify subtle features of the infiltration of fluids and/or feedback, and
Transport and isomorphic equilibria
Boozer, A.H.
1981-07-01
It is shown that large classes of plasma equilibria can have identical drift orbits and associated transport. Such equilibria are named isomorphic. In particular, the neoclassical transport coefficients are given for all equilibria in which the magnetic field strength depends on one helicity.
Transport and isomorphic equilibria
It is shown that large classes of plasma equilibria can have identical drift orbits and associated transport. Such equilibria are named isomorphic. In particular, the neoclassical transport coefficients are given for all equilibria in which the magnetic field strength depends on one helicity
Determination of CTX equilibria
The method by which we determine the magnetic field equilibrium for CTX in a nonperturbing manner is presented. Measurements of flux conserver image currents are combined with calculations from a numerical model of the equilibrium. Results give equilibria which differ significantly from the minimum energy state, but the equilibria data are well-described by a model where j/B has a linear dependence on the poloidal flux function. The observation of non-disruptive rotating internal kink distortions (with toroidal mode numbers n = 1, 2 and 3) within the equilibria and theoretical MHD thresholds for the onset of these modes corroborate the inferred equilibria
Highlights: ► Quaternary (liquid + liquid) equilibria are measured for ionic liquids, cyclohexane, pyridine and thiophene. ► Extraction of thiophene and pyridine from cyclohexane using ionic liquids is investigated. ► Three different ionic liquids are investigated. ► The experimental data can be successfully correlated using NRTL and UNIQUAC models. ► The experimental data are in moderate agreement with a priori predictions made using the COSMO-SAC model. -- Abstract: 1-Ethyl 3-methylimidazolium acetate [EMIM][OAc], 1-ethyl 3-methylimidazolium ethylsulfate [EMIM][EtSO4] and 1-ethyl 3-methylimidazolium methylsulfonate [EMIM][MeSO3] are found to be effective for the selective removal of a five member ring sulfur compound, viz. thiophene, and a six member ring nitrogen compound, viz. pyridine from a hydrocarbon, viz. cyclohexane at room temperature and atmospheric pressure. The liquid liquid equilibrium (LLE) data for the quaternary mixtures of ionic liquid (1) + thiophene (2) + pyridine (3) + cyclohexane (4) are experimentally determined. The experimental tie line data are successfully correlated with the Non Random Two Liquid (NRTL) and UNIversal QUAasi-Chemical (UNIQUAC) models, which provide a good correlation of the experimental data with root mean square deviation (RMSD) values less than unity for all the studied systems. The results suggest that the structure and size of the anion greatly affects the extractive performance of ionic liquids. The reliability of experimental data is ascertained by applying the quantum chemical based COnductor like Screening Model-Segment Activity Coefficient (COSMO-SAC) model. The goodness of the fit is determined by calculating the RMSD values. The RMSD values obtained for [EMIM][OAc], [EMIM][EtSO4] and [EMIM][MeSO3] are 10.4%, 8.1% and 12.2%, respectively
Meyer, Danilo; Neumann, Piotr; Koers, Eline; Sjuts, Hanno; Lüdtke, Stefan; Sheldrick, George M.; Ficner, Ralf; Tittmann, Kai
2012-01-01
Thiamin diphosphate, the vitamin B1 coenzyme, plays critical roles in fundamental metabolic pathways that require acyl carbanion equivalents. Studies on chemical models and enzymes had suggested that these carbanions are resonance-stabilized as enamines. A crystal structure of this intermediate in pyruvate oxidase at 1.1 Å resolution now challenges this paradigm by revealing that the enamine does not accumulate. Instead, the intermediate samples between the ketone and the carbanion both inter...
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.
Institutions, Equilibria and Efficiency
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...
Aim, Karel; Wichterle, Ivan
2010, s. 210. ISBN N. [International Conference on Properties and Phase Equilibria for Product and Process Design PPEPPD 2010 /20./. Suzhou (CN), 16.05.2010-21.05.2010] Institutional research plan: CEZ:AV0Z40720504 Keywords : esterification reactions * vapor-liquid equilibria * chemical equilibria Subject RIV: CF - Physical ; Theoretical Chemistry http://www.ppeppd2010.cn/
Resurrecting Equilibria Through Cycles
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....
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
Equilibria in saturated bentonite
It has been proposed that smectite clays, the predominant minerals in bentonite, are metastable solid solutions whose compositional heterogeneity prevents strict adherence to fixed ion activities and activity ratios characterizing invariant equilibria among stoichiometric phases. This is analysis of exceptionally well-constrained experimental data using a solid solution model defined by the phase rule and estimated ideal site-mixing are approached among smectite solid solutions and coexist metastably with respect to aSiO2(aq). Irreducible uncertainties are generated in the model by analytical and conceptual deficiencies in understanding compositional variability in smectite. However, their estimated effects on smectite's stability are relatively small, and are comparable to the effects of experimental uncertainty in standard Gibbs energies on the stabilities of stoichiometric minerals. An alternate analysis of the data further confirms that smectite does not behave like a stoichiometric phase. Ion-exchange models for this clay mineral may therefore be thermodynamically ill defined because stoichiometric behavior is assumed implicitly under limiting conditions of fixed sites. Ion exchange is a pragmatic simplification enabling empirical analysis of some experimental data. However, its empirical, rather than thermodynamic, basis should not be overextended to conditions that are beyond an experimentally calibrated range
Delavar M.
2012-01-01
Full Text Available In this study, adsorption of methane as the main constituent of natural gas was firstly studied on the pristine multi-walled carbon nanotubes (MWCNTs and then purification and chemical treatments of MWCNTs was performed to enhance the natural gas adsorption capacity. MWCNTs were chemically treated using different methods in this research. The results revealed that chemical treatment of the MWCNTs in presence of H2SO4/HNO3 acidic mixture in 3:1 volume ratio, enhanced considerably natural gas adsorption capacity (an optimal up to 45 mmol/g at temperature of 298.15 K and the pressure of 50 bar compared to the pristine MWCNTs (about 27 mmol/g at the same operating conditions. This effect can be attributed to the opening of the nanotubes caps with a major alteration in its structural properties due to chemical treatment. The experimental data of adsorption were almost equally well described by Langmuir, Freundlich and Sips equations to determine the model isotherms. The best fit was obtained by the Sips model isotherm with the r-squared value near to unity. Furthermore, using the experimental data obtained in different temperatures the isosteric heat of natural gas adsorption onto pristine MWCNTs was also calculated in the interested range of pressures and temperatures using the thermodynamic-based Clausius-Clapeyron equation from the Sips isotherm model. The results revealed an energetically heterogeneous surface of MWCNTs in natural gas adsorption. Also the natural gas adsorption process was kinetically studied through pseudo-second order and intra-particle diffusion models which indicated the intra-particular diffusion is rate limiting step in adsorption of methane on MWCNTs.
A large part of mechanical and durability characteristics of cement-based materials comes from the performances of the hydrated cement, cohesive matrix surrounding the granular skeleton. Experimental studies, in situ or in laboratory, associated to models, have notably enhanced knowledge on the cement material and led to adapted formulations to specific applications or particularly aggressive environments. Nevertheless, these models, developed for precise cases, do not permit to specifically conclude for other experimental conclusions. To extend its applicability domain, we propose a new evolutive approach, based on reactive transport expressed at the microstructure scale of the cement. In a general point of view, the evolution of the solid compounds of the cement matrix, by dissolutions or precipitations, during chemical aggressions can be related to the pore solution evolution, and this one relied to the ionic exchanges with the external environment. By the utilization of a geochemical code associated to a thermodynamical database and coupled to a 3D transport model, this approach authorizes the study of all aggressive solution. The approach has been validated by the comparison of experimental observations to simulated degradations for three different environments (pure water, mineralized water, seawater) and on three different materials (CEM I Portland cement with 0.25, 0.4 and 0.5 water-to cement ratio). The microstructural approach permits also to have access to mechanical properties evolutions. During chemical aggressions, the cement matrix evolution is traduced in a microstructure evolution. This one is represented from 3D images similarly to the models developed at NIST (National Institute of Standards and Technology). A new finite-element model, validated on previous tests or models, evaluates the stiffness of the cement paste, using as a mesh these microstructures. Our approach identifies and quantifies the major influence of porosity and its spatial
Lithium Alkyl Exchange Equilibria
Kinetic analyses of two types of exchange reactions of organo- lithium reagents, both alkyl and aryl types, RLi, have been made: (1) halogen-metal interchange with alkyl and aryl halides, R'X, and (2) hydrogen-metal interchange (commonly called metallation) with aromatic hydrocarbons, R'H. Rates of these RLi + R'X ⇄ RX + R'Li; (1) . RLi + R'H ⇄ RH+ R'Li (2) reactions have been determined, conditions under which the systems attain equilibrium have been established, and the positions of equilibrium measured, all as functions of the reactants, solvents and catalysts employed. Concerning halogen-lithium interchange between alkyl groups (1), the conclusion is reached that equilibration proceeds to yield the less sterically demanding alkyl group attached to lithium. The data show, for example, that isobutyllithium is much less stable than n-butyllithium, and again, that 2,6-dimethyl- phenyllithium is much less stable than phenyllithium. The exchange is general with iodides, occurs with some bromides and does not occur with chlorides. The exchange is quite slow in hydrocarbon media and is catalysed by relatively small amounts of ethers. In the presence of the optically active methyl ether of menthol, methyl iodide exchanges with racemic s-butyllithium to give optically active s-butyl iodide. In work with the second reaction, hydrogen-lithium interchange (2), nuclear magnetic resonance spectrometry has been used for rate studies. Catalysts (Lewis bases) have been evolved for establishing equilibria in rather unreactive systems, e.g. phenyllithium can be demonstrated to exchange with benzene by labelling the latter radioactivity. From the correlations of structure and reactivity found in this study, the conclusion is reached that the basic alkyllithium structure is dimeric, R2Li2 The arrangement of the groups within this dimer satisfactorily explain the special steric effects noted in organolithium reagent stability. (author)
Phase equilibria in polyethylene systems
Hemmingsen, Pål Viggo
2000-01-01
The background for this work is a need to better understand the production of high density polythylene (HDPE). HDPE particles grow in a loop slurry reactor, and particle swelling and slurry viscosity are critical parts in the process. This thesis is concerned with the thermodynamic aspects of liquid and solid polyethylene, and liquid-liquid and solid-liquid equilibria in solvent-polyethylene systems. It also covers studies of vapor-liquid and solid-liquid equilibria in solvent-n-alkane system...
Helical ITER hybrid scenario equilibria
Numerical computations of ITER equilibria in the hybrid scenario using a three-dimensional (3D) magnetohydrodynamic equilibrium code with nested magnetic flux surfaces demonstrate the formation of internal 3D helical cores similar to saturated ideal internal kink modes under reversed magnetic shear conditions when the minimum value of the inverse rotational transform is in the neighbourhood of unity.
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.
Equilibria, Fixed Points, and Complexity Classes
Yannakakis, Mihalis
2008-01-01
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or ...
Separating equilibria in continuous signalling games.
Bergstrom, Carl T.; Számadó, Szabolcs; Lachmann, Michael
2002-01-01
Much of the literature on costly signalling theory concentrates on separating equilibria of continuous signalling games. At such equilibria, every signaller sends a distinct signal, and signal receivers are able to exactly infer the signaller's condition from the signal sent. In this paper, we introduce a vector-field solution method that simplifies the process of solving for separating equilibria. Using this approach, we show that continuous signalling games can have low-cost separating equi...
Multiple equilibria in radiative-convective atmospheres
Rennó, Nilton O.
2011-01-01
A one-dimensional, radiative-convective model is used to study the equilibria conditions of moist atmospheres. We show that when the hydrologic cycle is included in the model a subcritical bifurcation occurs, leading to 2 linearly stable solutions to the radiative-convective equilibria. In this case, when the net forcing is larger than a critical value, two equilibria are possible. Furthermore, a finite amplitude instability can lead to a runaway greenhouse regime when the solar forcing is la...
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.
Fixed points and economic equilibria
Urai, Ken
2014-01-01
This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, a
Reflectivity method for geomechanical equilibria
Kuvshinov, Boris N.
2007-08-01
It is shown that the block LU decomposition of the transfer and scattering matrix convert these matrices into each other. This allows to introduce a generalization of the Kennett reflectivity method, which is applicable to arbitrary systems of linear differential equations. The introduced method is convenient to analyse equilibria, where the governing matrix is degenerate. The resulting algorithm is compact and numerically stable. To illustrate the concept, we consider elastic equilibrium of a layered medium. We also derive closed-form expressions for a quasi-stationary poroelastic case taking into account solid-fluid and electrokinetic coupling.
Phase equilibria in asymmetric mixtures
The simplified version of the Perturbed Hard-Chain Theory (SPHCT) is used to compute the phase equilibria and Henry's constants for mixtures in which the molecules are highly asymmetric both in shape and in the intermolecular potential. These mixtures include binary systems such as CO2/hydrocarbons and hydrocarbons/hydrocarbons, which are of particular interest for the oil industry. For this type of mixtures a single parameter (which is calculated from available experimental data of liquid-vapor equilibrium) is introduced. The approach yields results which compare well with the experimental behavior reported in the literature (Author)
Contemporaneous Perfect Epsilon-Equilibria
2003-01-01
We examine contemporaneous perfect epsilon-equilibria, in which a player’s actions after every history, evaluated at the point of deviation from the equilibrium, must be within epsilon of a best response. This concept implies, but is stronger than, Radner’s ex ante perfect epsilon-equilibrium. A strategy profile is a contemporaneous perfect epsilon-equilibrium of a game if it is a subgame perfect equilibrium in a perturbed game with nearly the same payoffs, with the converse holding for pure ...
Existence of Multiagent Equilibria with Limited Agents
Bowling, M; 10.1613/jair.1332
2011-01-01
Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in particular, the concept of Nash equilibria. Learners that directly learn an equilibrium obviously rely on their existence. Learners that instead seek to play optimally with respect to the other players also depend upon equilibria since equilibria are fixed points for learning. From another perspective, agents with limitations are real and common. These may be undesired physical limitations as well as self-imposed rational limitations, such as abstraction and approximation techniques, used to make learning tractable. This article explores the interactions of these two important concepts: equilibria and limitations in learning. We introduce the question of whether equilibria continue to exist when agents have limitations. We look at the general effects limitations can have on agent b...
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. PMID:25935748
Motion Control along Relative Equilibria
Nordkvist, Nikolaj
2008-01-01
The subject of this thesis is control of mechanical systems as they evolve along the steady motions called relative equilibria. These trajectories are of interest in theory and applications and have the characterizing property that the system's body-fixed velocity is constant. For example, constant......-speed rotation about a principal axis is a relative equilibrium of a rigid body in three dimensions. We focus our study on simple mechanical control systems on Lie groups, i.e., mechanical systems with the following properties: the configuration manifold is a matrix Lie group, the total energy is equal to the...... Lie group is locally controllable along a relative equilibrium. These conditions subsume the well-known local controllability conditions for equilibrium points. Second, for systems that have fewer controls than degrees of freedom, we present a novel algorithm to control simple mechanical control...
Beam-induced tensor pressure tokamak equilibria
D-shaped tensor pressure tokamak equilibria induced by neutral-beam injection are computed. The beam pressure components are evaluated from the moments of a distribution function that is a solution of the Fokker-Planck equation in which the pitch-angle scattering operator is ignored. The level-psub(perpendicular) contours undergo a significant shift away from the outer edge of the device with respect to the flux surfaces for perpendicular beam injection into broad-pressure-profile equilibria. The psub(parallel) contours undergo a somewhat smaller inward shift with respect to the flux surfaces for both parallel and perpendicular injection into broad-pressure-profile equilibria. For peaked-pressure-profile equilibria, the level pressure contours nearly co-incide with the flux surfaces. (author)
Braided magnetic fields: equilibria, relaxation and heating
Pontin, D I; Russell, A J B; Hornig, G
2015-01-01
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling. The key results obtained from recent modelling efforts are summarised, in the context of testable predictions for the laboratory. We discuss the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We discuss the properties of this relaxation, and in particular the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypo...
Braided magnetic fields: equilibria, relaxation and heating
Pontin, D. I.; Candelaresi, S.; Russell, A. J. B.; Hornig, G.
2016-05-01
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity—as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor’s hypothesis.
Nash equilibria via duality and homological selection
Arnab Basu; Samik Basu; Mahan MJ
2014-11-01
Given a multifunction from to the -fold symmetric product Sym$_{k}(X)$, we use the Dold–Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré duality in addition to the Dold–Thom theorem.
On Uniqueness of Equilibria in the CAPM
Thorsten HENS; Laitenberger, Jörg; Löffler, Andreas
2000-01-01
"- This paper replaces the paper ""Existence and Uniqueness of Equilibria in the CAPM"" -nIn the standard CAPM with a riskless asset we give a sufficient condition for uniqueness. This condition is a joint restriction on the agents' endowments and their preferences which is compatible with non-increasing absolute risk aversion and which is in particular satisfied with constant absolute risk aversion. Moreover in the CAPM without a riskless asset we give an example for multiple equilibria even...
Network Connection Games with Disconnected Equilibria
Brandes, Ulrik; Nick, Bobo
2008-01-01
In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost, and the utility is a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the utility for a pair of disconnected players to a finite value. Our analysis concentrates on existence, structure, and cost of disconnected regular and strong Nash equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected (strong) Nash equilibria can evolve. Components of these equilibria must be (strong) Nash equilibria of a smaller NCG. However, in contrast to the NCG, for almost all parameter values no tree is a stable componen...
Inefficient equilibria in transition economy
Igor Pospelov
1998-01-01
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 ArrowÃ¢Â€Â“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 ArrowÃ¢Â€Â“Debreu one, too. The implications for firms' integration and applicability to Russian economy are discussed.
大沼郁雄
2005-01-01
It is well known that the magnetic properties such as the Curie temperature TmagC and the mean magnetic moment β of ordered compounds have different values from those of the disordered solutions. For instance, both Tcmag and β of the Ni3 Pt (L12) and NiPt (L10) and Tcmag of the CoPt (L10) and CoPt3 (L12) ordered compounds are strongly depressed due to the ordering compared with those of the metastable disordered Ni-Pt and Co-Pt alloys. On the other hand, the γ-FeNi3(L12) and the α-FeCo (B2) ordered compounds have higher Tcmag and β values comparing with the disordered solution phases, γ (A1) and α (A2), respectively. In consequence, the stability of the ordered phase is depressed or enhanced due to the interaction between the chemical and magnetic ordering caused by the decrease or increase of Tcmag and β values. The purpose of this study is to investigate the effect of the interaction between the chemical and the magnetic ordering on the phase equilibria in the Fe-X(X=Al, Co, Ni, Rh, Si) binary systems.The Gibbs energy of the α(A2), γ(A1) and liquid phases is described by a sub-regular solution approximatior. The ordering contribution to the Gibbs energy ,ΔGmorder, and deviations of magnetic properties, ΔTcmag and Δβ, of the ordered compounds, FeAl(B2), Fe3 Al (D03), FeCo (B2), FeRh (B2), FeSi (B2), Fe3 Si (D03) and FeNi3 (L12) is introduced by the split compound energy formalism. Effect of the interaction between the chemical ordering, B2, D03 and L12 and the magnetic ordering on the phase equilibria will be discussed according to the calculated phase diagrams of the Fe-X binary systems.
Relative Equilibria of Identical Point Vortices
Aref, Hassan
2006-11-01
The problem of finding relative equilibria of identical point vortices is classical and was considered by Kelvin and J. J. Thomson almost immediately after the model had been introduced by Helmholtz in 1858. At the time relative equilibria of vortices were proposed as models of atoms. Apart from the intrinsic interest of the problem, and its mathematical challenge, such equilibria have been used as models for stationary states of distributed vortices, and have been observed in rotating superfluids, most recently in spectacular images of BECs. Simple equilibria such as regular polygons (both open and centered) were found and analyzed in the 19th century. Double rings and more recently triple rings have been found analytically. However, the numerically known relative equilibria continue to greatly outnumber those that are analytically known. A major numerical exploration was undertaken by Campell & Ziff in 1978 resulting in what is known as the Los Alamos Catalog. We will explore the results in this catalog and what we have learned since then, and present details on the quest for an analytical understanding of these intriguing states.
Why mixed equilibria may not be conventions
Hansen, Pelle Guldborg
2008-01-01
In his Convention (1969) David Lewis defined conventions as behavioural regularities instantiating proper coordination equilibria made salient by precedent and operational by this being common knowledge. While later proponents of game theoretical approaches in the study of convention have agreed on...... dropping Lewis' eccentric ‘coordination' requirement as well as that of common knowledge, they are confused on whether conventions should be regarded as proper thereby precluding mixed equilibria. In this paper I argue that mixed equilibria may not be conventions, but also suggest that the reason for this...... reveals that though common knowledge is not necessary for a convention to operate, it may be utilized as to identify the conventional aspect of a given practice....
Real Indeterminacy of Stationary Monetary Equilibria in Centralized Economies
Kamiya, Kazuya; Kubota, So; Nakajima, Kayuna
2011-01-01
In this paper, we present a new logic of indeterminacy of stationary monetary equilibria. We rst show that, in a class of dynamic Walrasian market models with at money, stationary equilibria are indeterminate; that is, there exists a continuum of stationary equilibria, where the value of money varies across the stationary equilibria. Then we explore the logic of the indeterminacy, and show that it can be applied not only to dynamic Walrasian market models but also to Jean et al. (2010)'s sear...
Effect of temperature on acid–base equilibria in separation techniques. A review
Gagliardi, Leonardo G.; Tascon, Marcos; Castells, Cecilia B., E-mail: castells@isis.unlp.edu.ar
2015-08-19
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.
Binary Solid-Liquid Phase Equilibria
Ellison, Herbert R.
1978-01-01
Indicates some of the information that may be obtained from a binary solid-liquid phase equilibria experiment and a method to write a computer program that will plot an ideal phase diagram to which the experimental results may be compared. (Author/CP)
Optimal Cartel Equilibria with Imperfect Monitoring
Dilip Abreu; David Pearce; Ennio Stacchetti
1984-01-01
There exist optimal symmetric equilibria in the Green-Porter model [5, 8] having an elementary intertemporal structure. Such an equilibrium is described entirely by two subsets of price space and two quantities, the only production levels used by firms in any contingency. The central technique employed in the analysis is the reduction of the repeated game to a family of static games.
On the stochastic stability of MHD equilibria
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.)
Phase equilibria of carbohydrates in polar solvents
Jonsdottir, Svava Osk; Rasmussen, Peter
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...
Equilibria with incompressible flows from symmetry analysis
Kuiroukidis, Ap
2015-01-01
We identify and study new nonlinear axisymmetric equilibria with incompressible flow of arbitrary direction satisfying a generalized Grad Shafranov equation by extending the symmetry analysis presented in [G. Cicogna and F. Pegoraro, Phys. Plasmas Vol. 22, 022520 (2015)]. In particular, we construct a typical tokamak D-shaped equilibrium with peaked toroidal current density, monotonically varying safety factor and sheared electric field.
Stability of relative equilibria of three vortices
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 more...... involved. The only comprehensive analysis available in the literature, by Tavantzis and Ting [Phys. Fluids 31, 1392 (1988)], is not easy to follow nor is it very physically intuitive. The symmetry between the three vortices is lost in this analysis. A different analysis is given based on explicit formulas...... for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium. A graphical representation of the space of vortex circulations is introduced, and the resultants between various polynomials that enter the problem are...
Modeling of Phase Equilibria Containing Associating Fluids
Derawi, Samer; Kontogeorgis, Georgios
terms of an activity coefficient model or an equation of state. Our target in this thesis is to review and develop such models capable of describing qualitatively as well as quantitatively phase equilibria in multicomponent multiphase systems containing non-polar, polar, and associating compounds. The......–known cubic SRK equation of state and the association term proposed by Wertheim, typically employed in models like the various variations of SAFT. CPA has been shown in the past to be a successful model for phase equilibria calculations for systems containing water, hydrocarbons and alcohols. In Chapter 4...... of CPA for the cross-association energy and volume parameters. Different types of such combining rules have been suggested over the past years for association models such as SAFT. These are tested in this work for CPA in terms of their correlation and prediction capabilities for vapor...
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.
Set identification in models with multiple equilibria
Marc Henry; Alfred Galichon
2011-01-01
We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily imp...
Quality of equilibria in resource allocation games
Jong, de, J.
2016-01-01
In situations where multiple parties are involved, local or selfish decisions result in outcomes that rarely align with what is best for society. In order to evaluate the quality of the resulting outcomes, we first need to predict which outcomes can occur. Game theory offers answers to this question, the Nash equilibrium being the most prominent example: it is an outcome where no party can improve by unilateral deviations. In that sense Nash equilibria are a good description of a stable outco...
Phase equilibria in stratified thin liquid films stabilized by colloidal particles
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-spher...
Quantum Nash Equilibria and Quantum Computing
Fellman, Philip Vos; Post, Jonathan Vos
In 2004, At the Fifth International Conference on Complex Systems, we drew attention to some remarkable findings by researchers at the Santa Fe Institute (Sato, Farmer and Akiyama, 2001) about hitherto unsuspected complexity in the Nash Equilibrium. As we progressed from these findings about heteroclinic Hamiltonians and chaotic transients hidden within the learning patterns of the simple rock-paper-scissors game to some related findings on the theory of quantum computing, one of the arguments we put forward was just as in the late 1990's a number of new Nash equilibria were discovered in simple bi-matrix games (Shubik and Quint, 1996; Von Stengel, 1997, 2000; and McLennan and Park, 1999) we would begin to see new Nash equilibria discovered as the result of quantum computation. While actual quantum computers remain rather primitive (Toibman, 2004), and the theory of quantum computation seems to be advancing perhaps a bit more slowly than originally expected, there have, nonetheless, been a number of advances in computation and some more radical advances in an allied field, quantum game theory (Huberman and Hogg, 2004) which are quite significant. In the course of this paper we will review a few of these discoveries and illustrate some of the characteristics of these new "Quantum Nash Equilibria". The full text of this research can be found at http://necsi.org/events/iccs6/viewpaper.php?id-234
Relative Equilibria in the Spherical, Finite Density 3-Body Problem
Scheeres, D J
2016-01-01
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
Ruthenium redox equilibria: 1. Thermodynamic stability of Ru(III and Ru(IV hydroxides
Igor Povar
2016-04-01
Full Text Available On the basis of the selected thermodynamic data for Ru(III and Ru(IV compounds in addition to original thermodynamic and graphical approach used in this paper, the thermodynamic stability areas of sparingly soluble hydroxides as well as the repartition of their soluble and insoluble chemical species towards the solution pH and initial concentrations of ruthenium in heterogeneous mixture solid phase–saturated solution have been investigated. By means of the ΔG–pH diagrams, the areas of thermodynamic stability of Ru(III and Ru(IV hydroxides have been established for a number of analytical concentrations in heterogeneous mixtures. The diagrams of heterogeneous and homogeneous chemical equilibria have been used for graphical representation of complex equilibria in aqueous solutions containing Ru(III and Ru(IV. The obtained results, based on the thermodynamic analysis and graphic design of the calculated data in the form of the diagrams of heterogeneous chemical equilibria, are in good agreement with the available experimental data.
Calculation of Liquid Water-Hydrate-Methane Vapor Phase Equilibria from Molecular Simulations
Jensen, Lars; Thomsen, Kaj; von Solms, Nicolas;
2010-01-01
Monte Carlo simulation methods for determining fluid- and crystal-phase chemical potentials are used for the first time to calculate liquid water-methane hydrate-methane vapor phase equilibria from knowledge of atomistic interaction potentials alone. The water and methane molecules are modeled...... using the TIP4P/ice potential and a united-atom Lennard-Jones potential. respectively. The equilibrium calculation method for this system has three components, (i) thermodynamic integration from a supercritical ideal gas to obtain the fluid-phase chemical potentials. (ii) calculation of the chemical...
On Stable Equilibria in Discrete-Space Social Interaction Models
AKAMATSU Takashi; Fujishima, Shota; Takayama, Yuki
2014-01-01
We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of...
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.
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.
Entropy and Equilibria in Competitive Systems
A. Y. Klimenko
2013-12-01
Full Text Available This paper investigates the applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for the characterisation of systems with transitive competition when mutations deviate from Gibbs mutations. Different types of equilibria in competitive systems are considered and analysed. As competition rules become more and more intransitive, thermodynamic analogies are eroded, and the behaviour of the system can become complex. This work analyses the phenomenon of punctuated evolution in the context of the competitive risk/benefit dilemma.
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
Natural elongation and triangularity of tokamak equilibria
Quasianalytic formulas are calculated for the elongation κ and triangularity δ of the plasma surface of a free-boundary tokamak equilibrium. The final results give κ and δ as functions of five quantities: the inverse aspect ratio ε, the poloidal beta βp, the internal inductance li, and the quadrupole and hexapole moments of the externally applied field. The agreement with numerically computed equilibria is found to be quite good when A≥3, κ≤1.5, and δ≤0.2 and when the plasma is limited by the vacuum vessel wall and not diverted by the presence of a separatrix on the plasma surface
Phase equilibria in Zr-Nb-Sn system
Using system approach to the analysis of phase equilibria in three-component system, as well as totality of author's experimental results and literature data, topology of phase diagram of Zr-Nb-Sn state in the region rich in zirconium is presented. In the system existence of four nonvariant equilibria is ascertained
Correlated Equilibria in Continuous Games: Characterization and Computation
Stein, Noah D.; Parrilo, Pablo A.; Ozdaglar, Asuman
2008-01-01
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions.
The use of radioisotopes for determination of complex equilibria
Radioisotopes can be used for determination of complex equilibria in solution, provided this solution is in equilibrium with another phase. The most versatile systems for studying aqueous solutions use solvent-extraction and ion-exchange methods. These two methods more seen be to universally practical for determining complex equilibria than EMF, spectrophotometric and other more conventional ones. (author)
Three-dimensional magnetohydrodynamic equilibria - I
By using an analytical method, the paper treats the three-dimensional magnetohydrodynamic equilibria of an incompressible, perfectly conducting plasma with an embedded magnetic field in the presence of a gravitational field. We derive a nonlinear second-order partial differential equation for the magnetic potential or stream function. According to the basic equation obtained by us, we analyse a simple example of solutions with the realistic physical property. This set of solutions represents a magnetohydrodynamic equilibrium model for the solar prominence. The results show that the z-component of the inertia force is everywhere upward, adding to upward the Lorentz force and pressure gradient in supporting the plasma weight in a magnetic well. (author)
An Algorithm for Computing All Berge Equilibria
H. W. Corley
2015-01-01
Full Text Available An algorithm is presented in this note for determining all Berge equilibria for an n-person game in normal form. This algorithm is based on the notion of disappointment, with the payoff matrix (PM being transformed into a disappointment matrix (DM. The DM has the property that a pure strategy profile of the PM is a BE if and only if (0,…,0 is the corresponding entry of the DM. Furthermore, any (0,…,0 entry of the DM is also a more restrictive Berge-Vaisman equilibrium if and only if each player’s BE payoff is at least as large as the player’s maximin security level.
CONSTRUCTING EXAMPLES WITH 5 EQUILIBRIA FOR SYMMETRIC 3 × 2 CES / LES PURE EXCHANGE ECONOMIES
Huang Hui; Shi Xiaojun; Zhang Shunming
2012-01-01
This paper explores the existence of multiple equilibria for symmetric 3 individual,2 good CES / LES pure exchange economies.Analytically,we show that there are no more than 5 equilibria in such economies.The number of equilibria varies from 5 to 3 then to 1.We generalize our analytical results of existence of 1,3,5 equilibria for a wide range of parametrizations.We also provide concrete examples of 1,3,5 equilibria with parameter zones specified.
The freedom to choose neutron star magnetic field equilibria
Glampedakis, Kostas
2016-01-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetised neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
The freedom to choose neutron star magnetic field equilibria
Glampedakis, Kostas; Lasky, Paul D.
2016-08-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetised neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
Learning Equilibria with Partial Information in Decentralized Wireless Networks
Rose, Luca; Lasaulce, Samson; Debbah, Mérouane
2011-01-01
In this article, a survey of several important equilibrium concepts for decentralized networks is presented. The term decentralized is used here to refer to scenarios where decisions (e.g., choosing a power allocation policy) are taken autonomously by devices interacting with each other (e.g., through mutual interference). The iterative long-term interaction is characterized by stable points of the wireless network called equilibria. The interest in these equilibria stems from the relevance of network stability and the fact that they can be achieved by letting radio devices to repeatedly interact over time. To achieve these equilibria, several learning techniques, namely, the best response dynamics, fictitious play, smoothed fictitious play, reinforcement learning algorithms, and regret matching, are discussed in terms of information requirements and convergence properties. Most of the notions introduced here, for both equilibria and learning schemes, are illustrated by a simple case study, namely, an interfe...
Sunspot equilibria in a monetary economy with capital accumulation
Bloise, Gaetano; Francesco MAGRIS
2000-01-01
In this paper, we consider the determinacy of equilibrium prices, interest rate and income in an economy with liquidity constraints and capital accumulation. In particular, we show that, even though no extrinsic uncertainty effects fundamentals, under some conditions, rational expectations equilibria exist in which prices and quantities exhibit repetitive and persistent fluctuations. To prove the existence of such sunspot equilibria, we introduce a technique of general applicability to nonlin...
Determination of 3D Equilibria from Flux Surface Knowledge Only
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
The freedom to choose neutron star magnetic field equilibria
Glampedakis, Kostas; Lasky, Paul D.
2016-01-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetised neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic ...
Solubility equilibria in chiral systems and their importance for enantioseparation
Lorenz, H; Sapoundjiev, D.; Seidel-Morgenstern, A.
2003-01-01
Ternary solubility equilibria are studied for three chiral systems in various aqueous and nonaqueous solvents. The chosen systems were a pharmaceutical intermediate, threonine and mandelic acid. Measured solubility data are presented and the nature of the ternary solubility phase diagrams is described. On this basis possible procedures for a crystallization based enantioseparation are derived. Also, the impact of solubility equilibria on the resolution of racemates by liquid chromatography is...
Medical Service
2002-01-01
It is reminded that all persons who use chemicals must inform CERN's Chemistry Service (TIS-GS-GC) and the CERN Medical Service (TIS-ME). Information concerning their toxicity or other hazards as well as the necessary individual and collective protection measures will be provided by these two services. Users must be in possession of a material safety data sheet (MSDS) for each chemical used. These can be obtained by one of several means : the manufacturer of the chemical (legally obliged to supply an MSDS for each chemical delivered) ; CERN's Chemistry Service of the General Safety Group of TIS ; for chemicals and gases available in the CERN Stores the MSDS has been made available via EDH either in pdf format or else via a link to the supplier's web site. Training courses in chemical safety are available for registration via HR-TD. CERN Medical Service : TIS-ME :73186 or service.medical@cern.ch Chemistry Service : TIS-GS-GC : 78546
Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations
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
Bhushanavathi, P.; Veeraswamy, B.; Rao, G. Nageswara; Viplavaprasad, U.
2012-01-01
Protonation equilibria of L-proline and L-valine in varying compositions (0.0-60.0% v/v) of 1, 2-Propanediol-water mixtures were investigated pH-metrically. Titrations were performed at 303.0 K and the ionic strength of the medium was maintained at 0.16 mol L-1 using sodium chloride. The best fit chemical models of the protonation equilibria were based on crystallographic R-factor, Χ2, skewness, and kurtosis. All the protonation constants of proline and valine increased with increasing propan...
Bilinear Relative Equilibria of Identical Point Vortices
Aref, H.; Beelen, Peter; Brøns, Morten
2012-01-01
-axis and n on the x-axis. We define generating polynomials q(z) and p(z), respectively, for each set of vortices. A second-order, linear ODE for p(z) given q(z) is derived. Several results relating the general solution of the ODE to relative equilibrium configurations are established. Our strongest result......A new class of bilinear relative equilibria of identical point vortices in which the vortices are constrained to be on two perpendicular lines, conveniently taken to be the x- and y-axes of a Cartesian coordinate system, is introduced and studied. In the general problem we have m vortices on the y......, 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...
The CHEASE code for toroidal MHD equilibria
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
Tearing Mode Stability of Evolving Toroidal Equilibria
Pletzer, A.; McCune, D.; Manickam, J.; Jardin, S. C.
2000-10-01
There are a number of toroidal equilibrium (such as JSOLVER, ESC, EFIT, and VMEC) and transport codes (such as TRANSP, BALDUR, and TSC) in our community that utilize differing equilibrium representations. There are also many heating and current drive (LSC and TORRAY), and stability (PEST1-3, GATO, NOVA, MARS, DCON, M3D) codes that require this equilibrium information. In an effort to provide seamless compatibility between the codes that produce and need these equilibria, we have developed two Fortran 90 modules, MEQ and XPLASMA, that serve as common interfaces between these two classes of codes. XPLASMA provides a common equilibrium representation for the heating and current drive applications while MEQ provides common equilibrium and associated metric information needed by MHD stability codes. We illustrate the utility of this approach by presenting results of PEST-3 tearing stability calculations of an NSTX discharge performed on profiles provided by the TRANSP code. Using the MEQ module, the TRANSP equilibrium data are stored in a Fortran 90 derived type and passed to PEST3 as a subroutine argument. All calculations are performed on the fly, as the profiles evolve.
Optimal equilibria of the best shot game
Dall'Asta, L; Ramezanpour, A
2010-01-01
We consider any network environment in which the "best shot game" is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game typically exhibits a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.
Grand Equilibrium: vapour-liquid equilibria by a new molecular simulation method
Vrabec, J
2009-01-01
A new molecular simulation method for the calculation of vapour-liquid equilibria of mixtures is presented. In this method, the independent thermodynamic variables are temperature and liquid composition. In the first step, one isobaric isothermal simulation for the liquid phase is performed, in which the chemical potentials of all components and their derivatives with respect to the pressure, i.e., the partial molar volumes, are calculated. From these results, first order Taylor series expansions for the chemical potentials as functions of the pressure $\\mu_i(p)$ at constant liquid composition are determined. That information is needed, as the specified pressure in the liquid will generally not be equal to the equilibrium pressure, which has to be found in the course of a vapour simulation. In the second step, one pseudo grand canonical simulation for the vapour phase is performed, where the chemical potentials are set according to the instantaneous pressure $p^v$ using the previously determined function $\\mu...
Applied chemical engineering thermodynamics
Tassios, Dimitrios P
1993-01-01
Applied Chemical Engineering Thermodynamics provides the undergraduate and graduate student of chemical engineering with the basic knowledge, the methodology and the references he needs to apply it in industrial practice. Thus, in addition to the classical topics of the laws of thermodynamics,pure component and mixture thermodynamic properties as well as phase and chemical equilibria the reader will find: - history of thermodynamics - energy conservation - internmolecular forces and molecular thermodynamics - cubic equations of state - statistical mechanics. A great number of calculated problems with solutions and an appendix with numerous tables of numbers of practical importance are extremely helpful for applied calculations. The computer programs on the included disk help the student to become familiar with the typical methods used in industry for volumetric and vapor-liquid equilibria calculations.
Phase equilibria in the uranium-chromium-carbon system
The alloys for this study (40 different compositions) were prepared by melting a charge comprising appropriate amounts of the various components and a 'master' alloy under an argon atmosphere on a water-cooled copper tray in an arc furnace equipped with a tungsten electrode. The starting components were uranium of 99.7% purity, graphite with an 0.004% ash content and electrolytically prepared chromium. The alloys were analysed by X-ray spectroscopy, X-ray diffraction analysis and microstructural methods, and a selective chemical analysis was made. As a result of these studies, a new compound of composition 45 at.%Cr - 10 at.%U - 45 at.%C was found; it was subjected to X-ray diffraction analysis. The composition of the compound x(UCr2C3) was refined. The crystallization characteristics of the alloys were established over the entire composition range, a diagram of the non- and monovariant equilibria was drawn and the section for the sub-solidus temperature was constructed over the entire range of concentrations. The isothermal section at 1500-16000C was constructed for the UC2-UC-UCrC2 region; this is characterized by a broad region consisting of a homogeneous solid solution of chromium in the high-temperature (UC-β-UC2) solid solution, which the chromium stabilizes down to a lower temperature. The observed increase of the carbon content in the solid solution with increase in the content of iron can apparently explain the improvement of chromium-modified monocarbide nuclear fuel reported in the literature. The carbon content in uranium-based monocarbide fuel can be increased to approximately 55 at.% by the addition of approximately 7 at.% chromium without change in the crystal structure. The parameters of the tetragonal (UC-β-UC2) lattice were determined to be a=5.041 A and c=5.128 A
Numerical computation of FCT equilibria by inverse equilibrium method
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)
The mechanics of rocking stones: equilibria on separated scales
Domokos, Gábor; Szabó, Tímea
2011-01-01
Rocking stones, balanced in counter-intuitive positions have always intrigued geologists. In our paper we explain this phenomenon based on high-precision scans of pebbles which exhibit similar behavior. We construct their convex hull and the heteroclinic graph carrying their equilibrium points. By systematic simplification of the arising Morse-Smale complex in a one-parameter process we show that equilibria occur typically in highly localized groups (flocks), the number of the latter can be reliably observed and determined by hand experiments. Both local and global (micro and macro) equilibria can be either stable or unstable. Most commonly, rocks and pebbles are balanced on stable local equilibria belonging to stable flocks. However, it is possible to balance a convex body on a stable local equilibrium belonging to an unstable flock and this is the intriguing mechanical scenario corresponding to rocking stones. Since outside observers can only reliably perceive flocks, the last described situation will appea...
(Solid + liquid) equilibria predictions of ionic liquid containing systems using COSMO-RS
Highlights: ► (Solid + liquid) equilibria (SLE) prediction on IL systems. ► Use of COSMO-RS model. ► Quantitative agreement with effect of temperature. - Abstract: (Solid + liquid) equilibria (SLE) prediction are an important phase equilibria property for ionic liquid (IL) mixtures especially when the IL exists as a solid. In this work, the SLE for the binary systems of (IL + thiophene) consisting of the ILs: n-butyl-4-methylpyridinium tosylate [BM4Py][TOS], n-butyl-3-methylpyridinium tosylate [BM3Py][TOS], n-hexyl-3-methylpyridinium tosylate [HM3Py][TOS], and 1,4-dimethylpyridinium tosylate [M1,4Py][TOS] are predicted using the quantum chemical based COSMO-RS (COnductor like Screening MOdel for Real Solvents) model. Initially, benchmarking studies are performed on binary mixtures which are known beforehand. The values of the predicted solubility are then compared with the experimental results by calculating the root mean square error (RMSE). The SLE predictions of the solubility of pyrene and dibenzothiophene in five different solvents were carried out giving an average RMSE of 4%. Further the applicability of COSMO-RS to binary systems consisting of (ionic liquid + alcohol) mixtures and (ionic liquid + hydrocarbons) are predicted. The ionic liquids concerned are n-butyl-3-methylpyridinium tosylate [BM3Py][TOS] while the alcohols and hydrocarbons are 1-butanol, 1-hexanol, 1-octanol, 1-decanol, and benzene, toluene, ethylbenzene, n-propylbenzene respectively. The experimental data for the ionic liquid [BM4Py][TOS] with thiophene gave the smallest deviation of 10.2%. The overall RMSE for IL–thiophene, IL–alcohol, and IL–hydrocarbons were 15%, 17.2% and 12.9% respectively. Thus the predicted solubility values were found to be in reasonable agreement with the experimental values.
Reaching Correlated Equilibria Through Multi-agent Learning
Cigler, Ludek; Faltings, Boi
2011-01-01
Many games have undesirable Nash equilibria. For exam- ple consider a resource allocation game in which two players compete for an exclusive access to a single resource. It has three Nash equilibria. The two pure-strategy NE are effi- cient, but not fair. The one mixed-strategy NE is fair, but not efficient. Aumann’s notion of correlated equilibrium fixes this problem: It assumes a correlation device which suggests each agent an action to take. However, such a “smart” coordination device migh...
Up-down asymmetric tokamak equilibria with parallel flows
A class of exact axisymmetric tokamak equilibria with sheared flows parallel to the magnetic field is constructed, generalizing previous work on the subject (Kuiroukidis 2010 Plasma Phys. Control. Fusion 52 015002). The additional free parameters associated with new terms in the solution make it possible to construct up–down asymmetric configurations with a divertor X-point and desirable values of confinement figures of merit as the safety factor on the magnetic axis and plasma betas; in particular, we construct a number of ITER-pertinent equilibria. Their stability with respect to linear MHD perturbations is also examined by applying a sufficient condition.
Role of Exchange Equilibria in Structural Chemistry
Although much of the past effort on the study of exchange reactions has been devoted to the scrambling of monofunctional substituents on a polyfunctional atom or moiety, complicated molecules may also undergo exchange of parts so as to give an equilibrium distribution of various molecular sizes and shapes. The use of high-resolution nuclear magnetic resonance (NMR) in investigating such equilibrated mixtures of compounds has been described in a number of 1964 and 1965 papers from the Monsanto Co. laboratory (see Refs [1-34] at the end of the abstracts). The systems thus studied include several new families of compounds; and the amounts and kinds of products resulting from the exchange reactions have been quantitatively described in terms of a small number of equilibrium constants. A new mathematical approach - that of stochastic graph theory [6] - has been employed to establish the form and the minimum number of equilibrium constants relating the non-cyclic structures and parts of molecular structures to each other. In addition, the equilibria between the cyclic and non-cyclic structures have been treated quantitatively. The emphasis in structural chemistry on the compounds of carbon (as evidenced by the division of descriptive chemistry into the organic and inorganic categories) is attributed to the fact that exchange reactions involving C-C bonds or bonds from carbon to any atom not exhibiting low-lying vacant bonding orbitals (e.g. Si, Ge, N, P, As. O, S, Se, F, Cl, Br) are exceedingly slow. On the other hand, there are vast areas of inorganic chemistry which have not previously been described because the molecules undergo such rapid exchange reactions that they cannot be separated. However, they can be identified and quantitatively assayed by means of physical methods (such as NMR) having short time constants, when the resulting data receive proper mathematical treatment - a procedure which is sufficiently involved to demand the use of a high-speed computer [6
Asset pricing puzzles explained by incomplete Brownian equilibria
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....
Shallow-water vortex equilibria and their stability
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 LD called the 'Rossby deformation length' relating the strength of stratification to that of the background rotation rate. Specifically, LD = c/f where c=√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.
From Singularity Theory to Finiteness of Walrasian Equilibria
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....
Computing Proper Equilibria of Zero-Sum Games
Miltersen, Peter Bro; Sørensen, Troels Bjerre
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....
Computation of Stackelberg Equilibria of Finite Sequential Games
Bosanski, Branislav; Branzei, Simina; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro; Sørensen, Troels Bjerre
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...
On Nash equilibria for noncooperative games governed by Burgers equation
Roubíček, Tomáš
2007-01-01
Roč. 132, č. 1 (2007), s. 41-50. ISSN 0022-3239 Grant ostatní: GA ČR(CZ) GA201/03/0934 Institutional research plan: CEZ:AV0Z10750506 Keywords : Nash equilibria * noncooperative games * Burgers equation Subject RIV: BA - General Mathematics Impact factor: 0.688, year: 2007
On Pure and (approximate) Strong Equilibria of Facility Location Games
Hansen, Thomas Dueholm
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. A special case of recently studied network design games, Facility Location merits separate study as a classic model with numerous applications and individual characteristics: our analysis for unweighted agents on metric networks reveals constant upper and lower bounds for the PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. Strong equilibria do not always exist, even for the unweighted metric case. For this cas...
Schäfer, Harald
2013-01-01
Chemical Transport Reactions focuses on the processes and reactions involved in the transport of solid or liquid substances to form vapor phase reaction products. The publication first offers information on experimental and theoretical principles and the transport of solid substances and its special applications. Discussions focus on calculation of the transport effect of heterogeneous equilibria for a gas motion between equilibrium spaces; transport effect and the thermodynamic quantities of the transport reaction; separation and purification of substances by means of material transport; and
Magnetoacoustic heating and FCT-equilibria in the belt pinch
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)
Phase equilibria, compatibility studies and thermal properties of beryllium systems
The quality control of commercial beryllium, the examinations of the phase equilibria in beryllium systems as well as the broad field of incompatibility and the reaction kinetics of beryllium with other materials necessitate a sophisticated method for the analysis of this element in micrometer areas. A powerful tool is the wavelength dispersive X-ray microanalyser. Therefore, a commercial synthetic Mo-B4C multilayer X-ray diffracting device with 2 d = 22.2 nm periodicity was used to extend X-ray microanalysis to the ultra-light elements Be and B in an existing instrument. The spectrometer covers a wavelength range between 5.2 and 13 nm. The wavelength of the Be Kα emission line from elemental Be is λ = 11.35 nm and the full width at half maximum is ΔE = 7.2 eV. The optimum working voltage Uo is 10 kV for moderate X-ray mass absorption of the targets. The determination of Be in oxides is less favourable owing to the high mass absorption. Uo has to be reduced to 5 kV. The chemical shift of the Be Kα line in BeO is Δλ = + 0.3 nm relative to pure Be. Beryllium pebbles are foreseen as neutron multipliers in future fusion reactor blanket concepts. Industrial intermediate Be products which had been produced by a modified Kroll process and subsequent reduction of BeF2 using Mg were investigated by X-ray microanalysis. The following precipitates in the Be matrix of 2 mm pebbles partially annealed up to 790 C could be detected: (Mg, Zr, U) Be13, MgBe13, Mg2Si, Al2Mg3 and (Fe, Cr) alloys. The maximum solubility of selected metallic impurities in beryllium annealed at 800 C is: 0.06 mass % Fe, 0.03 mass % Al, 0.02 mass % Si, 5Fe2, Be2C and Cr-Fe-Si were observed in specimens annealed between 870 and 690 C. It is interesting that Al5Fe2 precipitates were observed; however, the phase AlFeBe4 that would have been expected according to the phase diagram of the ternary Al-Be-Fe system was not found. Probably the Fe/Al ratio is too low for AlFeBe4 formation. The high annealing
Vapor–Liquid Equilibrium Coupled with Chemical Reaction (Transesterification)
Wichterle, Ivan; Aim, Karel
- : -, 2005 - (Domanska-Zelazna, U.; Malanowski, S.), s.68-69 ISBN 83-920719-1-3. [European Symposium on Applied Thermodynamics ESAT 2005 /21./. Jurata (PL), 01.06.2005-05.06.2005] R&D Projects: GA ČR(CZ) GA203/03/1588 Institutional research plan: CEZ:AV0Z40720504 Keywords : phase equilibria * chemical equilibria * transesterification Subject RIV: CF - Physical ; Theoretical Chemistry
Zaghloul, Mofreh R
2015-01-01
We investigate the dissociation and ionization equilibria of deuterium fluid over a wide range of temperatures and densities. The partition functions for molecular and atomic species are evaluated, in a statistical-mechanically consistent way, implementing recent developments in the literature and taking high-density effects into account. A new chemical model (free energy function) is introduced in which the fluid is considered as a mixture of diatomic molecules, atoms, ions and free electrons. Intensive short range hard core repulsion is taken into account together with partial degeneracy of free electrons and Coulomb interactions among charged particles. Samples of computational results are presented as a set of isotherms for the degree of ionization, dissociated fraction of molecules, pressure, and specific internal energy for a wide range of densities and temperatures. Predictions from the present model calculations show an improved and sensible physical behavior compared to other results in the literatur...
Reactive extraction of lactic acid using alamine 336 in MIBK: equilibria and kinetics.
Wasewar, Kailas L; Heesink, A Bert M; Versteeg, Geert F; Pangarkar, Vishwas G
2002-07-17
Lactic acid is an important commercial product and extracting it out of aqueous solution is a growing requirement in fermentation based industries and recovery from waste streams. The design of an amine extraction process requires (i) equilibrium and (ii) kinetic data for the acid-amine (solvent) system used. Equilibria for lactic acid extraction by alamine 336 in methyl-iso-butyl-ketone (MIBK) as a diluent have been determined. The extent to which the organic phase (amine +MIBK) may be loaded with lactic acid is expressed as a loading ratio, z=[HL](o)/[B](i,o). Calculations based on the stoichiometry of the reactive extraction and the equilibria involved indicated that more lactic acid is transferred to the organic phase than would be expected from the (1:1) stoichiometry of the reaction. The extraction equilibrium was interpreted as a result of consecutive formation of two acid-amine species with stoichiometries of 1:1 and 2:1. Equilibrium complexation constant for (1:1) and (2:1) has been estimated. Kinetics of extraction of lactic acid by alamine 336 in MIBK has also been determined. In a first study of its kind, the theory of extraction accompanied by a chemical reaction has been used to obtain the kinetics of extraction of lactic acid by alamine 336 in MIBK. The reaction between lactic acid and alamine 336 in MIBK in a stirred cell falls in Regime 3, extraction accompanied by a fast chemical reaction occurring in the diffusion film. The reaction has been found to be zero order in alamine 336 and first order in lactic acid with a rate constant of 1.38 s(-1). These data will be useful in the design of extraction processes. PMID:12052683
Experimental measurements of vapor-liquid equilibria of the H2O + CO2 + CH4 ternary system
Qin, J.; Rosenbauer, R.J.; Duan, Zhenhao
2008-01-01
Reported are the experimental measurements on vapor-liquid equilibria in the H2O + CO2 + CH4 ternary system at temperatures from (324 to 375) K and pressures from (10 to 50) MPa. The results indicate that the CH4 solubility in the ternary mixture is about 10 % to 40 % more than that calculated by interpolation from the Henry's law constants of the binary system, H2O + CH4, and the solubility of CO2 is 6 % to 20 % more than what is calculated by the interpolation from the Henry's law constants of the binary mixture, H 2O + CO2. ?? 2008 American Chemical Society.
Solid-liquid equilibria in the systems ClF5-BF3 and BrF5-BF3
The method of differential thermal analysis has been used to investigate solid-liquid equilibria in the systems ClF5-BF3 and BrF5-BF3 in the whole range of concent-- rations of components. No formation of chemical compounds is found. BrF5-BF3 system refers to the series of simple systems of the eutectic type and is characterized by eutectics depleted in bromine pentafluoride content (less than 5 mol. %) with the melting temperature close to melting temperature of pure boron trifluoride. In the ClF5-BF3 system components are mutually insoluble in both liquid and solid states
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.
Extended Group Contribution Model for Polyfunctional Phase Equilibria
Abildskov, Jens
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 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......-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...
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
Throumoulopoulos, George; Kuiroukidis, Apostolos; Tasso, Henri
2015-11-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis. This work has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018 under grant agreement No 633053.
On the extremum electric charge problem of steady electromagnetic equilibria
The existence of steady electromagnetic equilibria has earlier been predicted in terms of an extended formulation of Maxwell's equation. In this connection of variational problem was formulated for finding extremum values of the total electric charge of such equilibria in the axisymmetric case. In this paper the variational procedure has been cast into a new form, in terms of a generating function F. This simplifies the variational procedure substantially, by incorporating the field equations of the electric and magnetic potentials into the integrals of the charge qo, the magnetic moment Mo, the mass mo and the angular momentum so of the system. As a result, the variational procedure reduces to finding extremum values of qo, by varying F under the constraints of a given asymptotic form of F at infinity, and of one quantum condition. At this stage it appears possible for a set of extremum values of qo to arise from such a procedure. (au)
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Tasso, H
2015-01-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure
Kuiroukidis, Ap, E-mail: kouirouki@astro.auth.gr [Technological Education Institute of Serres, 62124 Serres (Greece); Throumoulopoulos, G. N., E-mail: gthroum@uoi.gr [Department of Physics, University of Ioannina, GR 451 10 Ioannina (Greece); Tasso, H., E-mail: het@ipp.mpg.de [Max-Planck-Institut für Plasmaphysik, D-85748 Garching (Germany)
2015-08-15
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation
Raimondi, A.; Tebaldi, C.
2008-04-01
A general n-node network is considered for which, in absence of interactions, each node is governed by a logistic equation. Interactions among the nodes take place in the form of competition, which also includes adaptive abilities through a (short term) memory effect. As a consequence the dynamics of the network is governed by a system of n2 nonlinear ordinary differential equations. As a first step, equilibria and their stability are investigated analytically for the general network in dependence of the relevant parameters, namely the strength of competition, the adaptation rate and the network size. The existence of classes of invariant subspaces, related to symmetries, allows the introduction of a reduced model, four dimensional, where n appears as a parameter, which give full account of existence and stability for the equilibria in the network.
Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria
Satoh, Atsuhiro; Tanaka, Yasuhito
2014-01-01
We analyze Bertrand and Cournot equilibria in an asymmetric oligopoly with more than two firms in which the firms produce differentiated substitutable goods and seek to maximize their relative profits instead of their absolute profits. Assuming linear demand functions and constant marginal costs we show the following results. If the marginal cost of a firm is lower (higher) than the average marginal cost over the industry, its output at the Bertrand equilibrium is larger (smaller) than that a...
Low-aspect-ratio toroidal equilibria of electron clouds
Toroidal electron clouds with a low aspect ratio (as small as 1.3) and lasting for thousands of poloidal rotation periods have been formed in the laboratory. Characteristic toroidal effects like a large inward shift of the minor axis of equipotential contours, elliptical and triangular deformations, etc., have been observed experimentally for the first time. The results of new analytic and numerical investigations of low-aspect-ratio electron cloud equilibria, which reproduce many of the observed features, are also presented
Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit
Pavel Hub\\xe1ek; Sunoo Park
2014-01-01
In this work we apply methods from cryptography to enable any number of mutually distrusting players to implement broad classes of mediated equilibria of strategic games without the need for trusted mediation. Our implementation makes use of a (standard) pre-play "cheap talk" phase, in which players engage in free and non-binding communication prior to playing in the original game. In our cheap talk phase, the players execute a secure multi-party computation protocol to sample an action profi...
Magnetic coordinates for equilibria with a continuous symmetry
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
Settling the Complexity of Computing Two-Player Nash Equilibria
Chen, Xi; Deng, Xiaotie; Teng, Shang-Hua
2007-01-01
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. This is the first of a series of results concerning the complexity of Nash equilibria. In particular, we prove the following theorems: Bimatrix does not have a fully polynomial-time approximation scheme unless every ...
What are the equilibria in linear public-good experiments?
Wolff, Irenaeus
2016-01-01
Most social-preference models have been tailored to yield only a full-defection equilibrium in one-shot linear public-good situations. This paper determines the Nash-equilibrium sets that result from experiment participants’ elicited preferences. The data show that multiple equilibria are relatively frequent even in a standard three-player setting. In this perspective, the common finding of close-toomnilateral defection at the end of repeated public-good games is surprising and raises the que...
Phase equilibria in alloys of Cr-Hf-N system
Metallographic, X-ray phase and differential thermal analyses are used to study phase equilibria in alloys of the Cr-Hf-N system with nitrogen concentration less than 15% (at.). Isothermal section at 1150 deg C is plotted. The polythermal Cr-HfN section is stated to be quasibinary eutectic one. Maximal solubility of HfN in chromium is estimated by thermodynamic calculation
Exchange Equilibria on the Surface of Ionic Crystals
New experimental data obtained by tracer techniques are presented and discussed. The number of exchanging cations and anions per unit area on the surface of BaSO4 and SrSO4 was measured for equivalent particles, cationic particles and anionic particles. Equivalent particles obtained by washing the precipitates thoroughly with water showed constant ratios of exchanging cations and anions per unit area of the surface. For cationic particles and anionic particles obtained by treatmeni of the precipitates with solutions containing barium ions or sulphate ions respectively, the ratio of the numbers of exchanging cations and anions was changed to higher values (cationic particles) or to lower values (anionic particles). From the values obtained the number of potential determining ions on the surface was determined. In the case of SrSO4 the numbers of exchanging cations and anions per unit area of the surface were measured as a function of temperature. They were found to decrease rapidly below 40°C in water solutions. This is explained by the immobilization of the water molecules on special points of the surface (in cracks for instance) proceeding gradually on approaching the freezing point. In agreement with this explanation the immobilization starts at lower temperatures for water-methanol mixtures. The exchange equilibria between different cations have been measured on the surface of the alkaline earth carbonates and sulphates and on the surface of the alkali tetraphenylborates. The equilibrium constants for these heterogeneous exchange reactions are discussed. In general these equilibria show the same trend as the solubilities. Barium ions, for instance, are enriched on the surface of strontium sulphate. The ratio of the solubilities, however, is no measure for these equilibria. The exchange equilibria on the surface of the alkaline earth sulphates show ''ideal'' behaviour; they are independent of the lattice parameters. (author)
Beltrami–Bernoulli equilibria in plasmas with degenerate electrons
Berezhiani, V. I., E-mail: vazhab@yahoo.com [Andronikashvili Institute of Physics, TSU, Tbilisi 0177, Georgia and School of Physics, Free University of Tbilisi, Tbilisi 0131, Georgia (United States); Shatashvili, N. L., E-mail: shatash@ictp.it [Andronikashvili Institute of Physics, TSU, Tbilisi 0177, Georgia and Department of Physics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University (TSU), Tbilisi 0179, Georgia (United States); Mahajan, S. M., E-mail: mahajan@mail.utexas.edu [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2015-02-15
A new class of Double Beltrami–Bernoulli equilibria, sustained by electron degeneracy pressure, is investigated. It is shown that due to electron degeneracy, a nontrivial Beltrami–Bernoulli equilibrium state is possible even for a zero temperature plasma. These states are, conceptually, studied to show the existence of new energy transformation pathways converting, for instance, the degeneracy energy into fluid kinetic energy. Such states may be of relevance to compact astrophysical objects like white dwarfs, neutron stars, etc.
Beltrami-Bernoulli Equilibria in Plasmas with Degenerate Electrons
Berezhiani, V I; Mahajan, S M
2014-01-01
A new class of Double Beltrami-Bernoulli equilibria, sustained by electron degeneracy pressure, are investigated. It is shown that due to electron degeneracy, a nontrivial Beltrami-Bernoulli equilibrium state is possible even for a zero temperature plasma. These states are, conceptually, studied to show the existence of new energy transformation pathways converting, for instance, the degeneracy energy into fluid kinetic energy. Such states may be of relevance to compact astrophysical objects like white dwarfs, neutron stars etc.
Existence of equilibria in quantum Bertrand-Edgeworth duopoly game
Sekiguchi, Yohei; Sato, Takashi
2010-01-01
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.
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.
Consistent expectations equilibria and learning in a stock market
Sögner, Leopold; Mitlöhner, Johann
1999-01-01
In this article we investigate the question whether the highly demanding informative requirements of rational expectations models are necessary to derive equilibria within capital market models. In the analysis agents are only provided with publicly available information such as prices and dividends. Nevertheless, we require that agents should behave like econometricians. Additionally, we skip the assumption of rational expectations models that agents know the implied law of motion of the sys...
Long-term Nash equilibria in electricity markets
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)
(Liquid + liquid) equilibria of perfluorocarbons with fluorinated ionic liquids
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
Preference Games and Personalized Equilibria, with Applications to Fractional BGP
Poplawski, Laura J; Sundaram, Ravi; Teng, Shang-Hua
2008-01-01
We study the complexity of computing equilibria in two classes of network games based on flows - fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fractional BGP games (Haxell, Wilfong), is a matter of practical importance. BBC games (Laoutaris et al) follow in the tradition of the large body of work on network formation games and capture a variety of applications ranging from social networks and overlay networks to peer-to-peer networks. The central result of this paper is that there are no fully polynomial-time approximation schemes (unless PPAD is in FP) for computing equilibria in both fractional BGP games and fractional BBC games. We obtain this result by proving the hardness for a new and surprisingly simple game, the fractional preference game, which is reducible to both fractional BGP and BBC games. Generalizing both fractional BBC games and fractional BGP...
Highlights: ► Aromatic/aliphatic hydrocarbons separation by ionic liquids. ► Cosmo-SAC thermodynamic model for prediction of LLE by quantum chemical calculations. ► Predictions successful for some ionic liquids. ► Correlation by single parameter for other ionic liquids. ► Preliminary screening of additional ionic liquids for aromatic/aliphatic separation. - Abstract: The extraction of aromatic hydrocarbons from aliphatic hydrocarbons is an important problem. This process can be used to enhance the capacity of ethylene crackers by prior removal of aromatics that cannot be cracked. Ionic liquids have been investigated extensively for liquid–liquid extraction of aromatics from aliphatics. The choice of a suitable ionic liquid may be made by measuring liquid−liquid equilibria. However, the large number of ionic liquids, formed by the various cation and anion combinations, makes the experimental measurements expensive and time consuming. Hence, a predictive thermodynamic model called Cosmo-SAC that uses quantum chemical calculations for calculating liquid−liquid equilibria has been evaluated. A priori predictions are accurate for some ionic liquids and inaccurate for some ionic liquids. However, it has been shown that even when a priori predictions are inaccurate, the data can be correlated using a single parameter that is characteristic of the ionic liquid and accurate predictions can be made for additional aromatic/aliphatic combinations for the same ionic liquid. A comparison with the NRTL and UNIQUAC models has also been carried out. In addition, a preliminary screening of ionic liquids for aromatic/aliphatic separations has been carried out using the Cosmo-SAC model. Finally, the “Cosmo” files for eight cations and sixteen anions corresponding to 128 potential ionic liquids have been provided for the use of the general scientific community to predict any thermodynamic equilibria involving ionic liquids without the use of any molecular modeling
Bernatová, Svatoslava; Aim, Karel; Wichterle, Ivan
2006-01-01
Roč. 247, 1-2 (2006) , s. 96-101. ISSN 0378-3812 R&D Projects: GA ČR(CZ) GA203/03/1588 Institutional research plan: CEZ:AV0Z40720504 Keywords : esterification * chemical equilibria * phase equilibria Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.680, year: 2006
Computation of thermodynamic equilibria of nuclear materials in multi-physics codes
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)
Thermodynamic assessment of hydrothermal alkali feldspar-mica-aluminosilicate equilibria
Sverjensky, D.A.; Hemley, J.J.; d'Angelo, W. M.
1991-01-01
The thermodynamic properties of minerals retrieved from consideration of solid-solid and dehydration equilibria with calorimetric reference values, and those of aqueous species derived from studies of electrolytes, are not consistent with experimentally measured high-temperature solubilities in the systems K2O- and Na2O-Al2O3-SiO2-H2O-HCl (e.g., K-fs - Ms - Qtz - K+ - H+). This introduces major inaccuracies into the computation of ionic activity ratios and the acidities of diagenetic, metamorphic, and magmatic hydrothermal fluids buffered by alkali silicate-bearing assemblages. We report a thermodynamic analysis of revised solubility equilibria in these systems that integrates the thermodynamic properties of minerals obtained from phase equilibria studies (Berman, 1988) with the properties of aqueous species calculated from a calibrated equation of state (Shock and Helgeson, 1988). This was achieved in two separate steps. First, new values of the free energies and enthalpies of formation at 25??C and 1 bar for the alkali silicates muscovite and albite were retrieved from the experimental solubility equilibria at 300??C and Psat. Because the latter have stoichiometric reaction coefficients different from those for solid-solid and dehydration equilibria, our procedure preserves exactly the relative thermodynamic properties of the alkali-bearing silicates (Berman, 1988). Only simple arithmetic adjustments of -1,600 and -1,626 (??500) cal/mol to all the K- and Na-bearing silicates, respectively, in Berman (1988) are required. In all cases, the revised values are within ??0.2% of calorimetric values. Similar adjustments were derived for the properties of minerals from Helgeson et al. (1978). Second, new values of the dissociation constant of HCl were retrieved from the solubility equilibria at temperatures and pressures from 300-600??C and 0.5-2.0 kbars using a simple model for aqueous speciation. The results agree well with the conductance-derived dissociation
Cismondi, Martin; Mollerup, Jørgen M.; Zabaloy, Marcelo S.
2010-01-01
available interaction parameters) in modern equations of state.In particular, the phase equilibria of binary mixtures containing CO2 and heavy n-alkanes have been studied by an important number of authors and using different types of models, achieving only partially accurate results and realizing the...... for the first time a quite successful complete description of asymmetric CO2+n-alkane binary systems, with n-alkane carbon number from 14 to 22....... a great diversity of mixtures. Nevertheless, the models for representing phase equilibria and physico-chemical properties of asymmetric systems may require more flexible mixing rules than the classical quadratic van der Waals (vdW) mixing rules or their equivalent (with regard to the number of...
Close pairs of relative equilibria for identical point vortices
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 found...... for 3n + 1 vortices, where n = 2, 3, ..., 30. A sufficient, although apparently not necessary, condition for this phenomenon of close solutions is that the "core" of the configuration is marginally stable, as occurs for a central vortex surrounded by an equilateral triangle. The open, regular heptagon...
Solitonlike solutions of magnetostatic equilibria: Plane-symmetric case
Yoshino, Hirotaka
2008-01-01
We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions, respectively, and $z$ is the direction of plane symmetry. Although such solutions are unstable against the numerical iteration, we give the procedure to realize the sufficient convergence. Our result provides the definite answer for the existence of the solitonlike solutions that was questioned in recent years. The method developed in this paper will make it possible to study the axisymmetric solitonlike solutions of the nonlinear GS equation, which could model astrophysical jets with knotty structures.
Thermodynamic calculation of phase equilibria in Cr - V - N alloys
PHase equilibria in the Cr-V-N system alloys using the thermodynamic calculation method are investigated. It is shown that Cr2N and V2N nitrides at the 1073 K temperature form a continuous series of solid solutions. Free energy of VNsub(0.42) nitride formation at the 1073 K temperature is determined to be equal - 44.4+-3 kJ/mol V. By the thermodynamic calculation method the isothermal cross section of the Cr-V-N phase diagram is plotted. The calculation results the limits of measurements error coincide with the experimental results
Analytical calculation of boozer magnetic coordinates for axisymmetric MHD equilibria
A new analytical technique for extracting the Boozer magnetic coordinates in axisymmetric MHD equilibria is described. The method is based upon the correspondence between the expansion of the flux function in toroidal multipolar moments and the expansion in toroidal axisymmetric harmonics of the magnetic scalar potential χ0, which appears in the covariant representation B=∇χ0+β∇ψ-T of the magnetic field. An example of calculation of Boozer magnetic coordinates is given for an experimental highly shaped high β equilibrium of DIIID
Anomeric and tautomeric equilibria in D-2-glucosamine Schiff bases
Kołodziej, B.; Grech, E.; Schilf, W.; Kamieński, B.; Makowski, M.; Rozwadowski, Z.; Dziembowska, T.
2007-11-01
The structure of some glucosamine Schiff bases has been studied by means of ab initio RHF and DFT calculation and CP/MAS 13C and 15N NMR measurements. The anomeric and tautomeric equilibria in a DMSO solution have been studied by 1H, 13C and 15N NMR spectroscopy. The anomeric composition of D-2-glucosamine Schiff bases in the solid state and in DMSO solution has been shown to depends on the tautomeric form of Schiff bases and electronic properties of substituents on the aromatic ring.
Phase Equilibria Relationships of High-Tc Superconductors
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
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
Existence of Nash equilibria in sporting contests with capacity constraints
平井, 秀明; ヒライ, シュウメイ; HIRAI, SHUMEI
2014-01-01
The main purpose of this paper is to demonstrate the existence of pure-strategy Nash equilibria in an “n” team sporting contest. Since the seminal papers of Szymanski (2003, 2004) and Szymanski and Késenne (2004), the Nash equilibrium model has been used in the analysis of professional team sports. However, many papers have been restricted to a two-team league model (Chang and Sanders, 2009; Cyrenne, 2009; Dietl et al., 2009). Dietl et al. (2008) that is considered a more general n-team...
Phase equilibria in the In–Sb–Bi system at 300 ºC
DUSKO MINIC
2006-07-01
Full Text Available Binary thermodynamic data, successfully used for phase diagram calculations of the binary systems In–Sb, Bi–Sb and In–Bi, were used fort the prediction of phase equilibria in the ternary system In–Sb–Bi at 300 ºC. The predicted equilibria were compared with the results of SEM–EDX analysis.
Stability and bifurcations of relative equilibria of a pendulum suspended on the equator
Burov, A. A.; Kosenko, I. I.
2013-05-01
The problem of equilibria of a pendulum suspended at an equatorial point relative to the rotating Earth is considered. An altitude is determined at which the degree of instability of the inverted pendulum changes from two to unity. Relative equilibria are investigated that bifurcate from the radial one when its degree of instability changes. Their stability properties are studied.
The Structure of the Set of Equilibria for Two Person Multicriteria Games
Borm, P.E.M.; Vermeulen, D.; Voorneveld, M.
1998-01-01
In this paper the structure of the set of equilibria for two person multicriteria games is analysed. It turns out that the classical result for the set of equilibria for bimatrix games, that it is a finite union of polytopes, is only valid for multicriteria games if one of the players only has two p
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
Equilibria, Dynamics and Current Sheets Formation in Magnetically Confined Coronae
Rappazzo, A F
2015-01-01
The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows that their magnetic fields have an asymmetric structure in the axial direction with variation length-scale $z_\\ell \\sim \\ell B_0/b$, where $B_0$ is the intensity of the strong axial guide field, $b$ that of the orthogonal magnetic field component, and $\\ell$ the scale of $\\mathbf{b}$. Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length $z_\\ell \\gtrsim L_z$, and increasingly more asymmetric for smaller variation scales $z_\\ell \\lesssim L_z$. The $critical$ $length$ $z_\\ell \\sim L_z$ corresponds to the magnetic field intensity threshold $b \\sim \\ell B_0/L_z$. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore fields with intensities below such t...
High temperature interdiffusion and phase equilibria in U-Mo
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 UO2 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 U2Mo 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 U2Mo 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 U2Mo phase boundary on the high uranium side are indicated from both the new and published interdiffusion data. 9 refs., 10 figs., 3 tabs
Self-consistent diverted tokamak equilibria with nonzero edge current
Shi Bing-Ren
2012-01-01
The semi-analytical method,previously used to construct model double-null and single-null diverted tokamak equilibria (Bingren Shi,Plasma Phys.Control Fusion 50 (2008) 085006,51 (2009) 105008,Nucl.Fusion 51 (2011) 023004),is extended to describe diverted tokamak equilibria with nonzero edge current,including the Pfirsch-Schlüter(PS) current.The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region.The model equilibrium is expressed by only two terms of the exact separable solutions of the GradShafranov equation,one of which is governed by a homogeneous ordinary differential equation,and the other by an inhomogeneous one.The particular merits of such a model configuration are that the internal region inside the separatrix and a suitable scrape-off layer can be simultaneously described by this exact solution.To investigate the physics in the region near the X-point,the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.
On Pure and (approximate) Strong Equilibria of Facility Location Games
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 ag......-approximate (e = 2.718...) strong equilibria and an upper bound of O(ln W) on SPoA (W is the sum of agents’ weights), which becomes tight Θ(ln n) for unweighted agents. Center for Algorithmic Game Theory, funded by the Carlsberg Foundation, Denmark.......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...... networks we prove upper and lower bounds on PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. We also prove a constant upper bound for the SPoA of metric networks when strong equilibria exist. For the weighted game on general networks we prove existence of e...
Stability of Hall equilibria in neutron star crusts
Marchant, Pablo; Reisenegger, Andreas [Instituto de Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul 7820436, Santiago (Chile); Valdivia, Juan Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile Casilla 653, Santiago (Chile); Hoyos, Jaime H., E-mail: pablo@astro.uni-bonn.de [Departamento de Ciencias Básicas, Universidad de Medellín Cra. 87 # 30-65, Medellín (Colombia)
2014-12-01
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are 'Hall equilibria', i.e., field configurations that are unaffected by Hall drift. Here we address the crucial question of the stability of these equilibria through axially symmetric (two-dimensional (2D)) numerical simulations of Hall drift and ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D stability of a purely poloidal equilibrium, for which ohmic dissipation makes the field evolve toward an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution toward an attractor, just as the purely poloidal one.
Stability of Hall equilibria in neutron star crusts
Marchant, Pablo; Valdivia, Juan Alejandro; Hoyos, Jaime H
2014-01-01
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stab...
Stability of Hall equilibria in neutron star crusts
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are 'Hall equilibria', i.e., field configurations that are unaffected by Hall drift. Here we address the crucial question of the stability of these equilibria through axially symmetric (two-dimensional (2D)) numerical simulations of Hall drift and ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D stability of a purely poloidal equilibrium, for which ohmic dissipation makes the field evolve toward an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution toward an attractor, just as the purely poloidal one.
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, A.; Throumoulopoulos, G. N.
2016-04-01
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones.
Electronic structure and phase equilibria in ternary substitutional alloys
A reliable, consistent scheme to study phase equilibria in ternary substitutional alloys based on the tight-binding approximation is presented. With electronic parameters from linear muffin-tin orbital calculations, the computed density of states and band structures compare well with those from more accurate abinitio calculations. Disordered alloys are studied within the tight-binding coherent-potential approximation extended to alloys; energetics of ordered systems are obtained through effective pair interactions computed with the general perturbation method; and partially ordered alloys are studied with a novel simplification of the molecular coherent-potential approximation combined with the general perturbation method. The formalism is applied to bcc-based Zr-Ru-Pd alloys which are promising candidates for medical implant devices. Using energetics obtained from the above scheme, we apply the cluster- variation method to study phase equilibria for particular pseudo- binary alloys and show that results are consistent with observed behavior of electronic specific heat coefficient with composition for Zr0.5(Ru, Pd)0.5
Axisymmetric equilibria with pressure anisotropy and plasma flow
Throumoulopoulos, George; Evangelias, Achilleas
2015-11-01
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a free boundary and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018.
Swarm dynamics and equilibria for a nonlocal aggregation model
We consider the aggregation equation ρt − ∇ · (ρ∇K * ρ) = 0 in Rn, where the interaction potential K models short-range repulsion and long-range attraction. We study a family of interaction potentials for which the equilibria are of finite density and compact support. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. In particular, we consider a potential for which the corresponding equilibrium solutions are of uniform density inside a ball of Rn and zero outside. For such a potential, various explicit calculations can be carried out in detail. In one dimension we fully solve the temporal dynamics, and in two or higher dimensions we show the global stability of this steady state within the class of radially symmetric solutions. Finally, we solve the following restricted inverse problem: given a radially symmetric density ρ-bar that is zero outside some ball of radius R and is polynomial inside the ball, construct an interaction potential K for which ρ-bar is the steady-state solution of the corresponding aggregation equation. Throughout the paper, numerical simulations are used to motivate and validate the analytical results
Expansions of non-symmetric toroidal magnetohydrodynamic equilibria
Weitzner, Harold
2016-06-01
Expansions of non-symmetric toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are carried out for two cases. The first expansion is in a topological torus in three dimensions, in which physical quantities are periodic of period 2 π in y and z. Data is given on the flux surface x = 0. Despite the possibility of magnetic resonances the power series expansion can be carried to all orders in a parameter which measures the flux between x = 0 and the surface in question. Resonances are resolved by appropriate addition resonant fields, as by Weitzner, [Phys. Plasmas 21, 022515 (2014)]. The second expansion is about a circular magnetic axis in a true torus. It is also assumed that the cross section of a flux surface at constant toroidal angle is approximately circular. The expansion is in an analogous flux coordinate, and despite potential resonance singularities, may be carried to all orders. Non-analytic behavior occurs near the magnetic axis. Physical quantities have a finite number of derivatives there. The results, even though no convergence proofs are given, support the possibility of smooth, well-behaved non-symmetric toroidal equilibria.
An integrated chemical and stable-isotope model of the origin of Midocean Ridge Hot Spring Systems
Bowers, Teresa Suter; Taylor, Hugh P., Jr.
1985-01-01
Chemical and isotopic changes accompanying seawater-basalt interaction in axial midocean ridge hydrothermal systems are modeled with the aid of chemical equilibria and mass transfer computer programs, incorporating provision for addition and subtraction of a wide-range of reactant and product minerals, as well as cation and oxygen and hydrogen isotopic exchange equilibria. The models involve stepwise introduction of fresh basalt into progressively modified seawater at discrete temperature int...
Rickaby, R E M
2015-03-13
Life and the chemical environment are united in an inescapable feedback cycle. The periodic table of the elements essential for life has transformed over Earth's history, but, as today, evolved in tune with the elements available in abundance in the environment. The most revolutionary time in life's history was the advent and proliferation of oxygenic photosynthesis which forced the environment towards a greater degree of oxidation. Consideration of three inorganic chemical equilibria throughout this gradual oxygenation prescribes a phased release of trace metals to the environment, which appear to have coevolved with employment of these new chemicals by life. Evolution towards complexity was chemically constrained, and changes in availability of notably Fe, Zn and Cu paced the systematic development of complex organisms. Evolving life repeatedly catalysed its own chemical challenges via the unwitting release of new and initially toxic chemicals. Ultimately, the harnessing of these allowed life to advance to greater complexity, though the mechanism responsible for translating novel chemistry to heritable use remains elusive. Whether a chemical acts as a poison or a nutrient lies both in the dose and in its environmental history. PMID:25666070
Phenol and cresol (o-, m-, and p-) were selected as the adsorbates with different dipole moment (cresol > phenol, methyl being electron-drawing group) and solubility (phenol > cresol, methyl being hydrophobic group). Macropore polymers (NDA-1800 and XAD-4), hypercrosslinked polymers (NDA-100), and chemically modified adsorbents (NDA-150 and NDA-99), were comparatively used to investigate the adsorption properties including equilibria, thermodynamics and kinetics. First, all of the results about equilibria show that the adsorption data fit well to the Freundlich model. The adsorption capacity of NDA-99 and NDA-150 especially for phenol is larger in a certain extent than other three types of polymers. The hydrophobic interaction from large specific surface was mainly occurred, while the polar groups containing oxygen and amine markedly enhance the adsorption process via hydrogen interaction. Furthermore, the adsorption amount for NDA-99 and XAD-4 decrease linearly with the solubility of solutes tested. Then, the negative values of enthalpy demonstrate the predominantly exothermic and physical solid-extraction processes. Finally, the relatively more rapid adsorption process could be found onto NDA-150 than NDA-99, with the reason of the double larger pore size of the former. In conclusion, solubility of solute, together with surface area, pore size and modified groups, extremely exerts influences to the adsorption performances
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Stefan Liebscher
2011-05-01
Full Text Available We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. We provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.
Chess-Like Games May Have No Uniform Nash Equilibria Even in Mixed Strategies
Endre Boros
2013-01-01
Full Text Available Recently, it was shown that Chess-like games may have no uniform (subgame perfect Nash equilibria in pure positional strategies. Moreover, Nash equilibria may fail to exist already in two-person games in which all infinite plays are equivalent and ranked as the worst outcome by both players. In this paper, we extend this negative result further, providing examples that are uniform Nash equilibria free, even in mixed or independently mixed strategies. Additionally, in case of independently mixed strategies we consider two different definitions for effective payoff: the Markovian and the a priori realization.
Radionuclide equilibria between the aquatic environment and fish tissues
Equilibrium conditions are often assumed in dose and risk calculations based on the simple linear concentration factor model, a commonly used model in the study of contaminant flow through ecosystems. It has been argued that by using a power function model to describe radionuclide retention in fish, equilibrium may never be achieved under natural conditions, thereby violating the equilibrium requirement in the concentration factor model. Our results demonstrate uranium-series radionuclide equilibria in a natural population of common white sucker (Catostomus commersoni). Concentration factors indicated that 226Ra, 232Th, 230Th, and 228Th preferentially deposited in bone over muscle. Although 226Ra had the highest concentration in bone, 228Th yielded the highest concentration factors for water-to-bone transfer. 232Th may not be in equilibrium because of a growth dilution effect. (Copyright (c) 1997 Elsevier Science B.V., Amsterdam. All rights reserved.)
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, A
2016-01-01
A generalised Grad-Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of...
Navigable networks as Nash equilibria of navigation games
Gulyás, András; Bíró, József J.; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2015-07-01
Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.
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
Settling the Complexity of Computing Two-Player Nash Equilibria
Chen, Xi; Teng, Shang-Hua
2007-01-01
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. This is the first of a series of results concerning the complexity of Nash equilibria. In particular, we prove the following theorems: Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results demonstrate that, even in the simplest form of non-cooperative games, equilibrium computation and approximation are polynomial-time equivalent to fixed point computation. Our results also have two broad complexity implications in mathematical economics and operations res...
Three-dimensional equilibria in axially symmetric tokamaks.
Garabedian, Paul R
2006-12-19
The NSTAB and TRAN computer codes have been developed to study equilibrium, stability, and transport in fusion plasmas with three-dimensional (3D) geometry. The numerical method that is applied calculates islands in tokamaks like the Doublet III-D at General Atomic and the International Thermonuclear Experimental Reactor. When bifurcated 3D solutions are used in Monte Carlo computations of the energy confinement time, a realistic simulation of transport is obtained. The significance of finding many 3D magnetohydrodynamic equilibria in axially symmetric tokamaks needs attention because their cumulative effect may contribute to the prompt loss of alpha particles or to crashes and disruptions that are observed. The 3D theory predicts good performance for stellarators. PMID:17159158
Efficiently Finding Trends in Macroscopic MHD Stability Using Perturbed Equilibria
Comer, K. J.; Callen, J. D.; Hegna, C. C.; Turnbull, A. D.; Cowley, S. C.
2001-10-01
The effects of equilibrium shaping and profiles on long wavelength ideal MHD instabilities in toroidal plasmas are traditionally studied using numerical parameter scans. Previously, we introduced a new perturbative technique to explore these dependencies: assuming small equilibrium variations, new stability properties are found using a perturbation of the energy principle rather than with a traditional stability code. With this approach, stability dependencies can be efficiently examined without numerically generating complete MHD stability results for every set of parameters (which can be time-intensive for accurate representations of several configurations). Here, we briefly expand on previous successful perturbed stability analyses for screw pinch equilibria by discussing cases where the approach fails. Next, we extend the approach to toroidal geometry using the GATO and TOQ codes, and present cases that both validate the approach and suggest caution in its application.
Dynamic data evaluation for solid-liquid equilibria
Cunico, Larissa; Ceriani, Roberta; Kang, Jeong Won;
The accuracy and reliability of the measured data sets to be used in regression of model parameters is an important issue related to modeling of phase equilibria. It is clear that good parameters for any model cannot be obtained from low quality data. A thermodynamic consistency test for solid......-liquid systems using a relation between the solid and liquid activity coefficients for systems containing metals [1], where the data from the two phases are given were proposed. However, as consistency tests based on the Gibbs–Duhem equation are not feasible, new consistency tests have been developed [2]. Some...... of the developed tests were based in the quality tests proposed for VLE data by Kang et al. [3] and a methodology that combines solute activity coefficients in the liquid phase at infinite dilution and a theoretically based term to account for the non-ideality in dilute solutions are discussed. In...
Phase equilibria in the Ni-Co-Ga alloy system
Phase equilibria among the α (A1), α' (L12), β (B2), δ (Ni5Ga3) and ε (Ni13Ga9) phases at elevated temperatures and the existing composition region of the martensite phase at room temperature in the Ni-Co side of the Ni-Co-Ga system were examined by electron probe microanalysis (EPMA) using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that single-phase regions of the α, α' and β phases at 700 and 1000 deg. C exist in a wide composition range parallel to Ni-Co section and that the existing region of the martensite phase at room temperature is also located over a wide range in the β phase along the β + α (or α') two-phase region
Multiple equilibria of cross-equatorial Inertial jets
CHAO JiPing; LIU Fei
2007-01-01
Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial inertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equilibria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Multiple equilibria of cross-equatorial Inertial jets
2007-01-01
Based on the developed Anderson and Moore’s theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Complex Networks as Nash Equilibria of Navigation Games
Gulyás, András; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2014-01-01
The common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organised so that networks can perform their functions. One common function that many networks perform is targeted transport or navigation. Here with the help of game theory we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties of real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. They are navigation skeletons that we show are present in the Internet, {\\it E. coli} metabolic network, English word network, US airport network, and the Hungarian road network. The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse the navigation in the network.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
Ottaviani, M. [CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Tebaldi, C. [Lecce University (Italy). Dept. of Mathematics
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 {Delta}` and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of {Delta}` 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) 20 refs.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
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)
Phase equilibria and molecular interaction studies on (naphthols + vanillin) systems
Highlights: ► Phase equilibria of (naphthol + vanillin) systems have been studied for the first time. ► Eutectic type phase diagrams are obtained. ► Eutectic mixtures show nonideal behaviour. ► There is a weak molecular interaction between the components in the eutectic mixtures. ► α-Naphthol–vanillin eutectic is more stable as compared to β-naphthol–vanillin. - Abstract: Phase equilibria between (α-naphthol + vanillin) and (β-naphthol + vanillin) systems have been studied by thaw-melt method and the results show the formation of simple eutectic mixtures. Crystallization velocities of components and eutectic mixtures were determined at different stages under cooling. With the help of differential scanning calorimeter (DSC), the enthalpy of fusion of components and eutectic mixtures was determined and from the values excess thermodynamic functions viz., excess Gibbs free energy (GE), excess entropy (SE), excess enthalpy (HE) of hypo-, hyper- and eutectic mixtures were calculated. Flexural strength measurements were made in order to understand the non-ideal nature of eutectics. FT-IR spectral studies indicate the formation of hydrogen bond in the eutectic mixture. Anisotropic and isotropic microstructural studies of components, hypo-, hyper- and eutectic mixtures were made. Jackson’s roughness parameter was calculated and found to be greater than 2 suggesting the faceted morphology with irregular structures. The overall results have shown that there is a weak molecular interaction between the components in the eutectic mixtures and the (α-naphthol + vanillin) eutectic is more stable as compared to the (β-naphthol + vanillin) eutectic system.
Equilibria and stability in partially relaxed plasma-vacuum systems
We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions separated by ideal MHD barriers. The magnetic field in each region is Beltrami, ∇ x B = μB, and the pressure constant. Between regions the pressure, field strength, and rotational transform may have step changes at the ideal barrier. A principle motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically 3D equilibria, with nonzero internal pressure, using robust KAM surfaces as the barriers. This article chiefly addresses whether the stability of two interface configurations with continuous rotational transform, but vanishing interface separation, is different from the stability of a single interface configuration with jump in the rotational transform. To make the problem analytically tractable, we derive the equilibria and stability of a multi-interface plasma in a periodic cylinder, generalizing the cylindrical treatment of Kaiser and Uecker (2004 Q. J. Mech. Appl. Math. 57 1-17). For two interfaces with no jump in rotational transform, we show that one eigenmode has in-phase interface displacements, and an eigenvalue that converges to the single barrier case in the limit of vanishing interface width. The complementary eigenmode is out-of-phase, and highly unstable. Physically, the unstable eigenmode is driven by the parallel current, and caused by the high shear required to match the different rotational transform on each interface. In the limit that the interface separation vanishes, the shear and parallel current density become infinite, and the parallel current between the interfaces nonzero. Surfaces with out-of-phase displacements will then collide, unless the amplitude goes to zero as the interface separation goes to zero. These results suggest the hypothesis that KAM barriers with different irrational rotational transform on either side may be allowable without violating nonlinear stability
Observation of equilibria with a double magnetic axis in LHD
Plasma shape control is a major knob to investigate confinement as well as MHD characteristics of magnetically confined plasmas. LHD has a large flexibility to explore a configuration effect by using 6 independent coil systems. Elongation can be controlled by a quadrupole field. Experimental observation of moderate elongation has shown that confinement is degraded gradually in both prolate (vertically elongated) and oblate (horizontally elongated) configurations. Since the rotational transform is weaker in the core region than in the periphery in LHD, a theoretical analysis suggests that excess quadrupole field results in split of the magnetic axis. Then the internal separatrix like petals emerges. Further application of quadrupole field eventually realizes a doublet configuration with a double magnetic axis bounded by this separatrix. An analytics suggests that split of the magnetic axis starts beyond elongation κ of 1.6 in the prolate case. The role of separatrix is attracting interest in effect on confinement performance as well as physics of unstable manifold, which has motivated strong shaping experiment in LHD. Both shaping of prolate and oblate directions has been explored for NBI heated plasmas. In the strongly prolate case, the doublet image has been observed by a tangential soft X-ray camera. Available profile measurements of temperature and density have not provided the 2-dimensional profile, however, assumption of concentric surfaces with a single magnetic axis seems to contradict with experimental observations in the 1-dimensional measurements in the case with strong shaping. This suggests the existence of doublet magnetic surfaces. These complex equilibria cannot be treated by the numerical code, ex. VMEC, with an assumption of nested flux surfaces with a single magnetic axis. Characteristics of these eccentric equilibria have been investigated by the HINT code which does not assume existence of nested flux surfaces. Experimental and computational
Aluminum Deoxidation Equilibria in Liquid Iron: Part II. Thermodynamic Modeling
Paek, Min-Kyu; Pak, Jong-Jin; Kang, Youn-Bae
2015-10-01
Al deoxidation equilibria in liquid iron over the whole composition range from very low Al ([pct Al] = 0.0027) to almost pure liquid Al were thermodynamically modeled for the first time using the Modified Quasichemical Model in the pair approximation for the liquid phase. The present modeling is distinguished from previous approaches in many ways. First, very strong attractions between metallic components, Fe and Al, and non-metallic component, O, were taken into account explicitly in terms of Short-Range Ordering. Second, the present thermodynamic modeling does not distinguish solvent and solutes among metallic components, and the model calculation can be applied from pure liquid Fe to pure liquid Al. Therefore, this approach is thermodynamically self-consistent, contrary to the previous approaches using interaction parameter formalism. Third, the present thermodynamic modeling describes an integral Gibbs energy of the liquid alloy in the framework of CALPHAD; therefore, it can be further used to develop a multicomponent thermodynamic database for liquid steel. Fourth, only a small temperature-independent parameter for ternary liquid was enough to account for the Al deoxidation over wide concentration (0.0027 oxide saturation) were modeled, and relevant model parameters were optimized. By merging these Gibbs energy descriptions with that of Fe-Al binary liquid modeled by the same modeling approach, the Gibbs energy of ternary Fe-Al-O solution at metal-rich region was obtained along with one small ternary parameter. It was shown that the present model successfully reproduced all available experimental data for the Al deoxidation equilibria. Limit of previously used interaction parameter formalism at high Al concentration is discussed.
Guillon, E
2004-09-15
A large part of mechanical and durability characteristics of cement-based materials comes from the performances of the hydrated cement, cohesive matrix surrounding the granular skeleton. Experimental studies, in situ or in laboratory, associated to models, have notably enhanced knowledge on the cement material and led to adapted formulations to specific applications or particularly aggressive environments. Nevertheless, these models, developed for precise cases, do not permit to specifically conclude for other experimental conclusions. To extend its applicability domain, we propose a new evolutive approach, based on reactive transport expressed at the microstructure scale of the cement. In a general point of view, the evolution of the solid compounds of the cement matrix, by dissolutions or precipitations, during chemical aggressions can be related to the pore solution evolution, and this one relied to the ionic exchanges with the external environment. By the utilization of a geochemical code associated to a thermodynamical database and coupled to a 3D transport model, this approach authorizes the study of all aggressive solution. The approach has been validated by the comparison of experimental observations to simulated degradations for three different environments (pure water, mineralized water, seawater) and on three different materials (CEM I Portland cement with 0.25, 0.4 and 0.5 water-to cement ratio). The microstructural approach permits also to have access to mechanical properties evolutions. During chemical aggressions, the cement matrix evolution is traduced in a microstructure evolution. This one is represented from 3D images similarly to the models developed at NIST (National Institute of Standards and Technology). A new finite-element model, validated on previous tests or models, evaluates the stiffness of the cement paste, using as a mesh these microstructures. Our approach identifies and quantifies the major influence of porosity and its spatial
AGGREGATION OF NANOPARTICLES IN POLYPHASE MIXTURES — IMPACT ON PHASE EQUILIBRIA
Hebabcha, Mustapha; Miltgen, Morgane; Modaressi, Ali; Magri, Pierre; Ait-kaci, A.; Rogalski, Marek
2013-01-01
In this work we were concerned with the inﬂuence of dispersed nanoarticles (Nps) on liquid—liquid and solid—liquid phase equilibria. The cryoscopic depression due to the presence of Nps of silver (d
Aim, Karel; Lísal, Martin
2002. s. 1. [European Conference on Applied Thermodynamics ESAT 2002 /19./. 06.09.2002-10.09.2002, Santorini] Institutional research plan: CEZ:AV0Z4072921 Keywords : Simulation * Phase equilibria Subject RIV: CC - Organic Chemistry
Multiple equilibria, soil conservation investments and the resilience of agricultural systems
Antle, J.M.; Stoorvogel, J.J.; Valdivia, R.O.
2006-01-01
This paper provides a new explanation for the persistent land degradation in some parts of the world, despite the availability of seemingly effective soil conservation technologies.We demonstrate that soil conservation technologies may induce agricultural systems to exhibit equilibria characterized by both low and high levels of soil degradation. These two equilibria are separated by a threshold level of soil degradation beyond which a conservation investment will not yield a positive return....
Bertrand and price-taking equilibria in markets with product differentiation
Coloma, Germán
2008-01-01
In this paper we show that a homogeneous-product market with multiple Bertrand equilibria becomes a market with a single Bertrand equilibrium when we introduce a small degree of product differentiation. When differentiation tends to zero, that Bertrand equilibrium converges to the unique price-taking equilibrium of the homogeneous-product market, which is in turn one of the multiple Bertrand equilibria for that market.
Export Restrictions and Multiple Spatial Price Equilibria: Export Quotas for Wheat in Ukraine
Götz, Linde; Qiu, Feng; Gervais, Jean-Philippe; Glauben, Thomas
2013-01-01
Relatively few models exist that allow for regime-dependent spatial price equilibria. This paper focuses on temporary export restrictions during international commodity price peaks. Theory suggests that export restrictions have price insulating effects and lead to multiple spatial equilibria between domestic and world market prices. Our analysis is unique in that it tests for linear versus non-linear cointegration within a smooth transition cointegration model. Applying this model to the whea...
On the Equilibria of the Extended Nematic Polymers under Elongational Flow
Hong Zhou
2007-01-01
Full Text Available We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples the Maier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field are axisymmetric. This finding of axisymmetry significantly simplifies any procedure of obtaining experimentally observable equilibria.
Calculation of Binary Adsorption Equilibria: Hydrocarbons and Carbon Dioxide on Activated Carbon
Marcussen, Lis; Krøll, A.
1999-01-01
Binary adsorption equilibria are calculated by means of a mathematical model for multicomponent mixtures combined with the SPD (Spreading Pressure Dependent) model for calculation of activity coefficients in the adsorbed phase. The model has been applied successfully for the adsorption of binary ...... mixtures of hydrocarbons and carbon dioxide on activated carbons. The model parameters have been determined, and the model has proven to be suited for prediction of adsorption equilibria in the investigated systems....
Multiple Equilibria and Interfirm Macro-Externality: An Analysis of Sluggish Real Adjustment
Yew-Kwang Ng; Ying Wu
2004-01-01
In an imperfectly competitive economy, a continuum of equilibria at the firm level exists under certain analytical conditions (Ng 1986). Extending the earlier analysis of a representative firm, this paper shows that even if the condition for a continuum of equilibria is not exactly satisfied, the factors of price-adjustment costs, interfirm heterogeneity, and macro-externality can cause the economy to be stuck at the quasi macroequilibria after aggregate demand experiences a contractionary sh...
Phase equilibria in the system MoCl5-MoF5
Phase equilibria in system MoCl5-MoF5 are studied using the DTA and visual-polythermal methods, as well as roentgenography. The system is characterized by the formation of incongruent MoCl4F and congruent compounds MoCl3F2, MoCl2F3, MoClF4 and also by the presence of stable and metastable equilibria
Calculation of phase equilibria in ternary systems uranyl salt-water-organic solvent
Experience in modeling extraction equilibria in systems with uranyl nitrate and halogen acetates with oxygen-containing organic solvents and tributylphosphate is presented. A method of calculating the equilibria on the basis of thermodynamic approach was suggested, phase diagrams for 12 extractive mixtures being calculated. Comparative analysis with the known experimental data was concluded, efficiency of the systems, that had not been previously considered by experiments, was predicted
New investigation of phase equilibria in the system Al–Cu–Si
Ponweiser, Norbert; Richter, Klaus W.
2012-01-01
The phase equilibria and invariant reactions in the system Al–Cu–Si were investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA) and electron probe micro analysis (EPMA). Isothermal phase equilibria were investigated within two isothermal sections. The isothermal section at 500 °C covers the whole ternary composition range and largely confirms the findings of previous phase diagram investigations. The isothermal section at 700 °...
On the application of the NRTL method to ternary (liquid + liquid) equilibria
The use of the NRTL method for correlating experimental data in ternary (liquid + liquid) equilibria is considered. It is concluded that parameters obtained by direct correlation techniques have not a direct physical meaning. Also, it is shown that the resulting values for these parameters depend on the number of experimental points considered and on the particular calculation method employed. Thus, it is very risky to employ such parameters in predicting equilibria of other ternary mixtures
The Structure of the Set of Equilibria for Two Person Multicriteria Games
Borm, P.E.M.; Vermeulen, D.; Voorneveld, M.
1998-01-01
In this paper the structure of the set of equilibria for two person multicriteria games is analysed. It turns out that the classical result for the set of equilibria for bimatrix games, that it is a finite union of polytopes, is only valid for multicriteria games if one of the players only has two pure strategies. A full polyhedral description of these polytopes can be derived when the player with an arbitrary number of pure strategies has one criterion.
Nie, Xiaobing; Zheng, Wei Xing
2016-03-01
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings. PMID:25826814
Anufriev, Mikhail; Bottazzi, Giulio; Pancotto, Francesca
2005-05-01
We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return on investment, and one risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed through the market clearing condition. Individual demands are expressed as fractions of traders wealth and depend on traders forecasts about future price movement. Under these assumptions, we derive the stochastic dynamical system that describes the evolution of price and wealth. We study the cases in which one or two agents operate in the market, identifying the possible equilibria and discussing their stability conditions. The main novelty of this paper rests in the abstraction from the precise characterization of agents' beliefs and preferences. In this respect our results generalize several previous contributions in the field. In particular, we show that, irrespectively of agents' behavior, the system can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where heterogeneous agents hold finite shares of the aggregate wealth. Moreover, we show that all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the role of different parameters for the stability of equilibria and the selection principle governing market dynamics.
On the steady states of weakly reversible chemical reaction networks
Deng, Jian; Jones, Christopher; Feinberg, Martin; Nachman, Adrian
2011-01-01
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric compatibility class.
Bootstrap current for small aspect ratio TOKAMAK equilibria
Full text. We present equilibrium features of the very small ratio tokamak, TBR-2 E, with the aspect ratio of 1.6, which is being designed in Brazil - a joint project with the participation of the University of Sao Paulo, the State University of Campinas, and the National Institute for Space Research. The equilibria have been studied by using the SELENE-J code developed at JAERI, Japan, by Tokuda et al. We have concentrated our study on the determination of the stability limit by using the critical pressure criterion for ballooning stability and Mercier criterion for other MHD modes. The β-limit values were calculated for the case of the non-inductive current and found that its maximum lies at elongation of 1.7. Increasing the triangularity, the β-limit values increase, but the maximum continues to stay at the same value of elongation. We have also studied the effect of the neo-classical transport properties by changing the plasma temperature (or β values). In particular, we have studied the trapped particles and bootstrap current. We have found that at temperatures as low as 600 eV the transport is already in banana regime and that the bootstrap current may account for a significant part of the total plasma current. (author)
Equilibria of idealized confined astral microtubules and coupled spindle poles.
Ivan V Maly
Full Text Available Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.
Ion-exchange equilibria and diffusion in engineered backfill
Engineered backfill can add confidence to confinement times of high-level nuclear waste stored in geologic media. This paper discusses the design and operation of a unique radial-flow diffusion cell to determine ion migration rates in backfill material under realistic repository conditions. New experimental results were reported for diffusion of CsCl in a background of NaCl into compacted bentonite and bentonite/quartz mixtures. Representation of the measured diffusion rates by the traditional, homogeneous porous-medium model significantly underestimates cesium penetration distances into the backfill. Surface diffusion is suggested as an additional mechanism by which cations transport in swollen montmorillonite; the surface diffusion coefficients for cesium is determined to be approximately 10-7 cm2/s. An electrostatic site-binding model is developed for ion-exchange equilibria on montmorillonite clay. The effect of pH, ionic strength, and specific adsorption are evaluated and compared favorably to new, experimental exchange isotherms measured on disaggregated clay. The electrostatic site-binding model permits a prediction of the influence of backfill compaction on K/sub d/ values. We find that for strongly adsorbing cations, compactions has little effect. However, anions exhibit significant Donnan exclusion with clay compaction. 40 references, 12 figures
Local gyrokinetic Vlasov simulations with realistic tokamak MHD equilibria
A local gyrokinetic Vlasov simulation code GKV is extended to incorporate realistic tokamak equilibria including up-down asymmetry, which are produced by a free-boundary 2D Grad-Shafranov equation solver MEUDAS. By using a newly developed interface code IGS, two dimensional rectangular equilibrium data from MEUDAS is converted to straight-field-line flux coordinates such as Hamada, Boozer, and axisymmetric coordinates, which are useful for gyrokinetic micro-instability and turbulent transport analyses. The developed codes have been verified by a cross-code benchmark test using Cyclone-base-case like MHD equilibrium, where good agreement in the dispersion relation of ion temperature gradient (ITG) driven mode has been confirmed. The extended GKV is applied to two types of shaped plasmas expected in JT-60SA tokamak devices, i.e., ITER-like and highly-shaped plasmas, and ITG-mode stability and residual zonal-flow level are investigated. Through the detailed comparisons, more favorable stability properties against the ITG mode are revealed for the highly-shaped case, where the lower ITG-mode growth rate and higher residual zonal-flow levels compared to the ITER-like case are identified. (author)
Phase equilibria in the Ni-Fe-Ga alloy system
The phase equilibria, A2/B2 and B2/L21 (or D03) order-disorder transitions and martensitic transformation on the Ni-Fe side of the Ni-Fe-Ga system were examined by electron probe microanalysis (EPMA) and differential scanning calorimetric (DSC) measurement. The equilibrium compositions of interrelations mainly among the α (A2), β (B2), β' (L21 or D03), γ (A1) and γ' (L12) phases were determined using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that a bcc single-phase region composed of α, β and β' at 850-1000 deg. C exists in a wide composition range and that the critical temperature of the B2/L21 order-disorder transformation in the Fe3Ga-Ni3Ga pseudo-binary section gradually increases with increasing Ni content. The existing composition region of the martensite phase at room temperature was also determined by the diffusion triple method
Thermodynamically predicted oscillations in closed chemical systems
Zilbergleyt, B
2010-01-01
All known up to now models of chemical oscillations are based exclusively on kinetic considerations. The chemical gross-process equation is split usually by elementary steps, each step is supplied by an arrow and a differential equation, joint solution to such a construction under certain, often ad hoc chosen conditions and with ad hoc numerical coefficients leads to chemical oscillations. Kinetic perception of chemical oscillations reigns without exclusions. However, as it was recently shown by the author for the laser and for the electrochemical systems, chemical oscillations follow also from solutions to the basic expressions of discrete thermodynamics of chemical equilibria. Graphically those solutions are various fork bifurcation diagrams, and, in certain types of chemical systems, oscillations are well pronounced in the bistable bifurcation areas. In this work we describe a general thermodynamic approach to chemical oscillations as opposite to kinetic models, and depict some of their new features like s...
O'Hara, M. J.; Herzberg, C.
2002-06-01
The concentrations and ratios of the major elements determine the physical properties and the phase equilibria behavior of peridotites and basalts in response to the changing energy contents of the systems. The behavior of the trace elements and isotopic features are influenced in their turn by the phase equilibria, by the physical character of the partial melting and partial crystallization processes, and by the way in which a magma interacts with its wall rocks. Concentrating on the trace element and isotope contents of basalts to the exclusion of the field relations, petrology, major element data, and phase equilibria is as improvident as slaughtering the buffalo for the sake of its tongue. The crust is a cool boundary layer and a density filter, which impedes the upward transfer of hot, dense "primary" picritic and komatiitic liquids. Planetary crusts are sites of large-scale contamination and extensive partial crystallization of primitive melts striving to escape to the surface. Escape of truly unmodified primitive melts to the surface is a rare event, requiring the resolution of daunting problems in chemical and mechanical engineering. Primary status for volumetrically abundant basalts such as mid-ocean ridge basalt, ocean island basalt, and continental flood basalts is denied by their low-pressure cotectic character, first remarked upon on petrological grounds in 1928 and on experimental grounds in 1962. These basalt liquids are products of crystal-liquid separation at low pressure. Primary status for these common basalts is further denied by the phase equilibria of such compositions at elevated pressures, when the required residual mantle mineralogy (magnesian olivine and orthopyroxene) is not stable at the liquidus. It is also denied by the picritic or komatiitic nature of partial melts of candidate upper-mantle compositions at high pressures - a conclusion supported by calculation of the melt composition, which would need to be extracted in order to
Modelling of phase equilibria of glycol ethers mixtures using an association model
Garrido, Nuno M.; Folas, Georgios; Kontogeorgis, Georgios
2008-01-01
Vapor-liquid and liquid-liquid equilibria of glycol ethers (surfactant) mixtures with hydrocarbons, polar compounds and water are calculated using an association model, the Cubic-Plus-Association Equation of State. Parameters are estimated for several non-ionic surfactants of the polyoxyethylene......, Kamlet-Taft parameters and, perhaps most importantly, mixture liquid-liquid equilibria data with alkanes are used for choosing optimum parameter sets is illustrated. Vapor-liquid, liquid-liquid equilibria and second virial coefficient data are used for model validation, including aqueous and other cross-associating...... mixtures. The influence on the results of the association schemes, type of data available, combining rules for cross-associating mixtures and interaction parameters are discussed also in connection to other cross-associating mixtures, previously studied with the model. Finally, the capabilities and...
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
MHD Stability Trends from Perturbed Equilibria: Possible Limitations with Toroidal Geometry
Comer, K. J.; Callen, J. D.; Hegna, C. C.; Turnbull, A. D.; Cowley, S.
2003-10-01
The effects of equilibrium changes on ideal MHD properties are usually studied using numerical parameter scans. Previously, we introduced a new technique to explore these dependencies: changes in the potential energy δ W due to equilibrium changes are found with an expansion of the energy principle, rather than an eigenvalue-solver code. Validation of the approach in toroidal geometry attempted to use GATO (an ideal MHD stability code) and DIII-D shot 87009. The approach should succeed with the global modes of 87009; however, ˜ 0.1% changes to qo predicted δ W rapidly increasing. Perturbing β of other toroidal equilibria resulted in similar behavior. We first review results for a cylindrical equilibrium and for 87009. Between the cylindrical case and 87009 lie several other equilibria, which should produce intermediate results. We examine several of these intermediate equilibria, starting with the cylindrical case and changing aspect ratio, shape and profiles until ending at 87009.
A note on relative equilibria in a rotating shallow water layer
Ait Abderrahmane, Hamid
2013-05-08
Relative equilibria of two and three satellite vortices in a rotating shallow water layer have been recorded via particle image velocimetry (PIV) and their autorotation speed was estimated. This study shows that these equilibria retain the fundamental characteristics of Kelvin\\'s equilibria, and could be adequately described by the classical idealized point vortex theory. The same conclusion can also be inferred using the experimental dataset of Bergmann etÂ al.Â (J.Â FluidÂ Mech., vol. 679, 2011, pp. 415-431; J. Fluid Mech., vol. 691, 2012, pp. 605-606) if the assigned field\\'s contribution to pattern rotation is included. © 2013 Cambridge University Press.
Bernardo, Mario di; Camlibel, Kanat
2005-01-01
This paper is concerned with the structural stability of boundary equilibria in a class of hybrid systems, that of piecewise linear continuous systems. Specifically, we study the structural stability under parameter variations of equilibria lying on discontinuity boundaries in phase space dividing r
Phase Equilibria for extraction processes with designer solvents
Lago García de Dios, Sara
2013-01-01
In recent years, there has been an increasing concern about the effects of toxic chemicals in the environment. In response to this concern, there is a growing impetus to develop chemical manufacturing processes which can reduce or eliminate the use or generation of hazardous substances. Within this aspect of green chemistry, in this Thesis, Ionic Liquids (ILs) and Deep Eutectic Solvents (DESs) have been tested as greener alternatives in different chemical processes. In a ...
Studies of the chemical equilibria in the solvent extraction of uranium
Uranium was extracted with amines dissolved in diluents. Using alamine 336 as an extractant, dodecane as a diluent, and n-octanol as an additive for third phase inhibition, UO2++ extraction from H2SO4-Na2SO4 aqueous solutions was studied. When the extraction coefficient of uranium was plotted as a function of the initial Na2SO4 concentration at a constant sulfuric acid concentration, the typical initial spike type extraction curve was obtained in this case too. Thus, at low Na2SO4 concentrations, a reaction such as UO2SO4 + 2 (AlamineH)2SO4 reversible (AlamineH)4UO2(SO4)3...(1) is believed to take place, while at high Na2SO4 concentrations reaction (2) is thought to be occurring. UO2(SO4)34- + 2(R3NH)2SO4 reversible (R3NH)4UO2(SO4)3 = 2SO4-2...(2). The same result obtained with Na2SO4 as with H2SO4 is explained by the action of sulfate ions
Haubrock, J.; Raspe, M.; Versteeg, G.F.; Kooijman, H.A.; Taylor, R.; Hogendoorn, J.A.
2008-01-01
New experimental equilibrium data of the reaction of dimethyl carbonate (DMC) and phenol to methyl phenyl carbonate (MPC) and the subsequent disproportion and transesterification reaction of MPC to diphenyl carbonate (DPC) are presented and interpreted in terms of the reaction equilibrium coefficien
Chemical speciation and equilibria of some nucleic acid compounds and their iron(III) complexes
Masoud, Mamdouh S.; Abd El-Kaway, Marwa Y.; Hindawy, Ahmed M.; Soayed, Amina A.
The pH effect on electronic absorption spectra of some biologically active nucleic acid constituents have been studied at room temperature and the mechanism of ionization was explained. These compounds are of two categories (pyrimidines: [barbital; 5,5'-diethyl-barbituric acid], [SBA; 4,6-dihydroxy-2-mercapto-pyrimidin], [NBA; 5-nitro-2,4,6(1H,3H,5H)-pyrimidine trione] and [TU; 2,3-dihydro-2-thioxo-pyrimidin-4(1H)-one]) and (purines: [adenine; 6-amino purine], its [Schiff bases derived from adenine-acetylacetone; (Z)-4-(7H-purin-6-ylimino)pentan-2-one) and adenine-salicylaldehyde; 2-((7H-purin-6-ylimino) methyl) phenol] and its [Azo derived from adenine-resorcinol; 4-((7H-purin-6-yl)-diazenyl) benzene-1,3-diol]. The phenomena of tautomerization assigned different tautomers. Different spectrophotometric methods are applied to evaluate the pK's values that explained with their molecular structures. The interaction of Fe3+ with some selected pyrimidines (barbital, NBA and SBA) was explained using familiar six spectrophotometric methods. The data typified the existence of different absorbing species with the different stoichiometries 1:1, 1:2, 1:3 and 2:3. The stability constant of the complexes was computed. More approach was deduced to assign the existence of different species applying the distribution diagrams.
Sasidevan, V
2015-01-01
The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games - namely, those of Nash equilibrium and co-action equilibrium. For the Nash equilibrium, we show that the dynamical view can provide an equilibrium refinement, selecting one equilibrium among several possibilities, thereby solving the issue of multiple equilibria that appear in some games. We illustrate in detail this dynamical perspective by considering three well known 2-person games namely the Prisoner's Dilemma, game of Chicken and the Stag-Hunt. We find that in all of these cases, co-action equilibria tends to correspond to `nicer' strategies than those corresponding to Nash equilibria.
Experimental determination of phase equilibria in the Fe-Nb-V ternary system
The phase equilibria in the Fe-Nb-V ternary system were investigated by means of optical microscopy, electron probe microanalysis and X-ray diffraction. Four isothermal sections in the Fe-Nb-V ternary system at 1000 deg. C, 1100 deg. C, 1200 deg. C and 1300 deg. C were firstly experimentally established. Present experimental results indicate that: (1) there is a large (Nb, V) continuous bcc solid solution; (2) there are the larger solubilities of V in the FeNb and Fe2Nb phases. The newly determined phase equilibria in this system will provide important support for the development of hydrogen storage materials and microalloyed steels.
Analytic high-beta tokamak equilibria with poloidal-sonic flow and their stability
Full text: In magnetically confined plasmas, equilibrium flows may suppress instability and turbulent transport to give rise to the formation of transport barriers or pedestals. In axisymmetric toroidal systems like tokamaks, both of the poloidal and toroidal components of flow are important for these phenomena. The ideal magnetohydrodynamic (MHD) equations for equilibria with flow reduce to the so-called generalized Grad-Shafranov (GS) equation and the Bernoulli law with five free functions of the magnetic flux in axisymmetric systems. These systems of a nonlinear partial differential equation (PDE) and a nonlinear algebraic equation can be solved numerically by iteration schemes when the PDE is elliptic in the whole region. Recently, a new reduced set of equilibrium equations has been derived for high-beta tokamaks with flow in the order of the poloidal-sound velocity. This model includes the effect of poloidal flow on both the magnetic flux and the pressure in higher-order terms of asymptotic expansions in terms of the inverse aspect ratio. We have found analytical solutions for this reduced set of equations for linear profiles of the lowest order free functions and perform qualitative studies of equilibria with sub- and super-poloidal-sonic flow. Analytical representations of equilibria with flow may be useful for benchmarks and initial guesses of iteration as well as for qualitative studies of equilibrium flows and stability analyses. In this presentation, we will also discuss the stability of these analytical equilibria. Equilibrium flow brings non-Hermitian properties to linear perturbations. In contrast to the static equilibria, the variational formulation does not give necessary and sufficient conditions, and the growth and damping can be non-exponential where mode analysis does not work. Due to these reasons, stability analysis of equilibria with flow must be done more carefully than that of static equilibria. Based on the formalism of the reduced MHD
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Canale, Eduardo A., E-mail: ecanale@pol.una.py [Facultad Politénica, UNA, Asunción (Paraguay); Monzón, Pablo, E-mail: monzon@fing.edu.uy [School of Engineering, UDELAR, Montevideo 11300 (Uruguay)
2015-02-15
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Canale, Eduardo A.
2015-02-01
© 2015 AIP Publishing LLC. This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Theory of phase equilibria and critical mixing points in binary lipid bilayers
Risbo, Jens; Sperotto, Maria Maddalena; Mouritsen, Ole G.
1995-01-01
energy necessary to derive phase equilibria is determined from the simulations using distribution functions and histogram techniques, and the nature of the phase equilibria is determined by a finite-size scaling analysis which also permits the interfacial tension to be derived. Results are also presented...... for the enthalpy and the compositional fluctuations. It is shown, in accordance with experiments, that the nonideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively nonideal mixing behavior as the chain-length difference is increased. Moreover, indications...
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
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.
TOWARD A THEORY OF SUSTAINABLE SYSTEMS. FLUID PHASE EQUILIBRIA: JOURNAL ARTICLE
NRMRL/STD JOURNAL NRMRL-CIN-1364 Cabezas*, H., and Fath**, B.D. Toward a Theory of Sustainable Systems. Fluid Phase Equilibria (Nakanishi, K., Yasukiko, A., Miyano, Y. (Ed.), Elsevier Science B.V.) 194-197:3-14 (2002). EPA/600/J-02/186, www.elsevier.com/locate/fluid. 03/2...
High-pressure fluid-phase equilibria: Experimental methods and systems investigated (2000-2004)
Dohrn, Ralf; Peper, Stephanie; Fonseca, José
2010-01-01
-vapor-liquid equilibria, critical points, the solubility of high-boiling substances in supercritical fluids, the solubility of gases in liquids and the solubility (sorption) of volatile components in polymers are included. For the systems investigated, the reference, the temperature and pressure range of the data, and...
Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups
Nordkvist, Nikolaj; Bullo, F.
2008-01-01
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...
Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups
Nordkvist, Nikolaj; Bullo, Francesco
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...
On convergence to equilibria for the Keller-Segel chemotaxis model
Feireisl, Eduard; Laurencot, P.; Petzeltová, Hana
2007-01-01
Roč. 236, č. 2 (2007), s. 551-569. ISSN 0022-0396 R&D Projects: GA AV ČR(CZ) IAA100190606 Institutional research plan: CEZ:AV0Z10190503 Keywords : Keller-Segel chemotaxis model * convergence to equilibria * Łojasiewicz-Simon theory Subject RIV: BA - General Mathematics Impact factor: 1.097, year: 2007
Truth-telling and Nash equilibria in minimum cost spanning tree models
Hougaard, Jens Leth; Tvede, Mich
2012-01-01
to the rules of the game. We characterize ways of allocating costs such that true announcements constitute Nash equilibria both in case of full and incomplete information. In particular, we find that the Shapley rule based on the irreducible cost matrix is consistent with truthful announcements while...
The Representation of Highly Non-Ideal Phase Equilibria Using Computer Graphics.
Charos, Georgios N.; And Others
1986-01-01
Previous work focused on use of computer graphics in teaching thermodynamic phase equilibria for classes I and II. Extends this work to include the considerably more non-ideal phase behavior shown by classes III, IV, and V. Student and instructor response has been overwhelmingly positive about the approach. (JN)
Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion
Olaya, Maria del Mar; Reyes-Labarta, Juan A.; Serrano, Maria Dolores; Marcilla, Antonio
2010-01-01
Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…
Liquid-liquid equilibria for binary and ternary polymer solutions with PC-SAFT
Lindvig, Thomas; Michelsen, Michael Locht; Kontogeorgis, Georgios
2004-01-01
Two algorithms for evaluating liquid-liquid equilibria (LLE) for binary and ternary polymer solutions are presented. The binary algorithm provides the temperature versus concentration cloud-point curve at fixed pressure, whereas the ternary algorithm provides component 1 versus component 2...... accuracy, even by using interaction parameters obtained from binary vapor-liquid equlibrium data....
Phase equilibria study of binary systems comprising an (ionic liquid + hydrocarbon)
Highlights: • The (solid + liquid) equilibria (SLE) and (liquid + liquid) equilibria (LLE) study. • {[PMPyr][CF3SO3] + heptane, or benzene, or thiophene, or benzothiophene}. • {[BCN4Py][TCM] + heptane, or toluene, or 2-methylthiophene, or benzothiophene}. • Thermodynamic NRTL modelling. • Separation of sulfur compounds from alkanes and aromatics from aliphatics. - Abstract: In this study, the interaction of two ionic liquids with hydrocarbons has been investigated. With this aim, (solid + liquid) equilibria (SLE) and (liquid + liquid) equilibria (LLE) for binary systems of {1-methyl-1-propyl-pyrrolidinium triflate [PMPyr][CF3SO3] + heptane, or benzene, or thiophene, or benzothiophene} and {N-butyl-4-cyanopyridinium tricyanomethanide [BCN4Py][TCM] + heptane, or toluene, or 2-methylthiophene, or benzothiophene} were measured at ambient pressure. A dynamic method was used over a broad range of mole fractions and temperatures from (T = 270 to 370) K. An upper critical solution temperature (UCST) was detected for all mutually immiscible systems. The immiscibility gap for [BCN4Py][TCM] in benzene and thiophene is larger than those for [PMPyr][CF3SO3]. Conversely, in heptane it is slightly larger for [PMPyr][CF3SO3]. The basic thermal properties of the pure ILs, i.e. melting and glass-transition temperatures as well as the enthalpy of fusion have been measured using a differential scanning microcalorimetry technique (DSC). The well-known NRTL model has been used to correlate the experimental SLE data points
Peeling-Ballooning Mode Analysis in Shifted-Circle Tokamak Equilibria
Burke, B.; Kruger, S. E.; Hegna, C. C.; Snyder, P. B.; Sovinec, C. R.; Zhu, P.
2009-11-01
Progress in understanding edge localized modes (ELMs) has been made by investigating the stability properties of edge localized peeling-ballooning modes. We focus on the evolution of ideal MHD modes over a large spectrum in two shifted-circle tokamak equilibria, using the extended-MHD code NIMROD. The TOQ-generated equilibria model a H-mode plasma with a pedestal pressure profile and parallel edge currents. A vacuum region is prescribed by a resistivity profile that transitions from a small to very large value at a specified location. The vacuum model is benchmarked against the linear ideal MHD codes ELITE & GATO. We demonstrate vacuum effects on the stability by adjusting the vacuum location relative to the pedestal pressure region. Ballooning-like instabilities dominate distant vacuum cases, whereas peeling mode physics is expected to dominate as the vacuum approaches the pedestal. Numerical simulations of the early nonlinear stages of edge localized MHD instabilities are presented. Comparisons between equilibria that have ``ballooning'' dominated instabilities relative to equilibria that are ``peeling'' dominated are made.
Simulation of the high-pressure phase equilibria of hydrocarbon-water/brine systems
Zuo, You-Xiang; Stenby, Erling Halfdan; Guo, Tian-Min
1996-01-01
The major objectives of this work are: (1) extend the modified Patel-Teja (MPT) equation of state proposed for aqueous electrolyte systems (Zuo and Guo, 1991) to describe the liquid-liquid and vapor-liquid-liquid equilibria of hydrocarbon-water/brine systems through introducing an unconventional ...