Multiple Equilibrium Analysis Research Articles

Bifurcation, chaos, and their control in a wheelset model

In this paper, we present an improved wheelset motion model with two degrees of freedom and study the dynamic behaviors of the system including the symmetry, the existence and uniqueness of the solution, continuous dependence on initial conditions, and Hopf bifurcation. The dynamic characteristics of the wheelset motion system under a nonholonomic constraint are investigated. These results generalize and improve some known results about the wheelset motion system. Meanwhile, based on multiple equilibrium analysis, calculation of Lyapunov exponents and Poincaré section, the chaotic behaviors of the wheelset system are discussed, which indicates that there are more complex dynamic behaviors in the railway wheelset system with higher order terms of Taylor series of trigonometric functions. This paper has also realized the chaos control and bifurcation control for the wheelset motion system by adaptive feedback control method and linear feedback control. The results show that the chaotic wheelset system and bifurcation wheelset system are all well controlled, whether by controlling the yaw angle and the lateral displacement or only by controlling the yaw angle. Numerical simulations are carried out to further verify theoretical analyses.

Entropy in multiple equilibria, theory and applications.

Analysis of multiple equilibria where the binding enthalpy of the species is the same for all sites and independent of those that are already bonded delivers insight on the evolution of the entropy as the reactions proceed and explains why the equilibrium constants always decrease with increasing number of occupied sites. The validity of the results is independent of the nature of bonding. Consequences are explained by discussing dicarboxylic acids, cation exchange of zeolite A, and the insertion of guests into the one-dimensional channels of zeolite L, by cation exchange for cationic guests and from the gas phase for neutral molecules. The quantitative link between the description of multiple equilibria and Langmuir's isotherm equation provides new insight. We express the concentration dependence of fraction filling of guests on the length of the channels, a result which is important for understanding observations and planning the synthesis of new host-guest composites. The free reaction enthalpy can be split in the particle distribution term and all other contributions. The results are therefore relevant for analyzing and interpreting experimental data also of systems where the condition of constant binding enthalpy is not or only partially fulfilled.

Parameterization of linear supply functions in nonlinear AC electricity market equilibrium models - Part II: Case studies

This study utilizes the primal-dual nonlinear interior point algorithm formulated in Part I of this two-series paper, to obtain electricity market supply function equilibrium solutions for the bi-level market problem of nonlinear power systems with AC meshed networks. The strategic offers of the market players are modeled by parameterizing the generation marginal cost functions using any of the four available parameterization methods to obtain profit-maximizing linear supply function bids. The analysis takes into account a variety of test systems and examines the relation between the equilibrium solutions obtained from the different parameterization methods and the role of network complexity. An analysis of multiple equilibria in AC network constrained systems is also provided.

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Multiple Equilibrium Analysis Description of Adsorption on Na−Mordenite and H−Mordenite

Adsorption isotherms are reported for Na−mordenite and H−mordenite at several temperatures with a series of gas adsorptives above their critical temperature. The data sets are analyzed with the multiple equilibrium analysis (MEA) method [Drago, R. S.; et al. J. Am. Chem. Soc. 1998, 120, 538−547. Drago, R. S.; et al. J. Phys. Chem. B 1997, 101, 7548−7555], which produces equilibrium constants (Ki), capacities (ni), and thermodynamic parameters (enthalpies, ΔHi, and entropies, ΔSi) of adsorption for each process. The limited pore size distribution present in the zeolite mordenite presents an interesting comparison to the amorphous carbons studied previously by MEA [Drago, R. S.; et al. J. Phys. Chem. B 1997, 101, 7548−7555]. The results of the MEA description of the adsorption data gathered for the interaction of an adsorbate (particularly, N2, CO, and Xe) with Na−mordenite and H−mordenite are compared to other literature reports (including infrared spectroscopic studies and Monte Carlo simulations), and go...

The multiple equilibrium analysis quantitative prediction of single and multi-component adsorption isotherms on carbonaceous and zeolitic solids

The previously introduced multiple equilibrium analysis (MEA), which produces equilibrium constants ( K i ), capacities ( n i ), and thermodynamic parameters (enthalpies, Δ H i , and entropies, Δ S i ) of adsorption for each process, has been used to predict adsorption isotherms for N 2, CO, CH 4, C 2H 6, and SF 6 on one zeolitic (HZSM-5) and five carbonaceous (A-572, A-563, A-600, F-300, and BPL) solids. The adsorption of CO is best reproduced on each of the solids. In general, the adsorption of N 2 has been accurately predicted, while CH 4 and C 2H 6 are underpredicted and SF 6 is overpredicted. Previously reported high-pressure data for the adsorption of CH 4 on BPL was very accurately predicted. The application of the MEA prediction of adsorption behavior has quite a potential for a variety of applications. Adsorbents can be used for catalyst supports, gas separation, respiratory protection, environmental applications, and even have the potential for fuel storage capabilities. The prediction of adsorption performance will lead to a greater understanding of the fundamental interactions involved in these systems and will help create new and better systems.

Using the beta/alpha peak-height ratio of ATP in 31P NMR spectra to measure free [Mg2+]: theoretical and practical problems.

A recently described alternative method for determining free [Mg2+] in cells and tissue with 31P NMR spectroscopy, which is based on the peak-height ratio of the beta and alpha resonances of ATP (h(beta/alpha)) [J. Biol. Chem. 271, 21141-21150 (1996)], was found to have numerous problems. These problems include a flaw in the basic multiple equilibrium analysis, the inapplicability of the calibration curve to in vivo studies, and a lack of sensitivity of the measured ratio to changes in free [Mg2+] at 'clinical' field strengths. This suggests that the use of this procedure will be very limited.

Molecular Dimensions for Adsorptives

Pore volumes, accessible surface areas, and the thermodynamics of adsorption are essential in the understanding of solid surface characteristics fundamental to catalyst and adsorbent screening and selection. The recently developed Multiple Equilibrium Analysis (MEA) provides a thorough characterization of the adsorption process. Molecular properties such as molecular volumes and projected molecular areas are needed in order to convert moles adsorbed to surface volumes and probe dependent, accessible surface areas. These molecular quantities are also needed in conventional methods for determining areas and pore volumes. Generally, these molecular properties have been estimated from bulk properties, but many assumptions are required. As a result, different literature values are employed for these essential molecular properties. In this article, molecular structures for various conformers of many molecules are calculated using ZINDO. Molecular volumes and excluded molecular areas are determined from these st...

A Multiple-Process Equilibrium Analysis of Silica Gel and HZSM-5

Adsorption isotherms are reported for HZSM-5 and silica gel using a series of gas adsorptives at several temperatures above their critical temperature. The data are analyzed with a new multiple equilibria adsorption model producing equilibrium constants (Ki), capacities (ni), and enthalpies (−ΔHi) for each of the processes. Unlike the amorphous adsorbents studied earlier, which contain a distribution of pore sizes, zeolitic materials have uniform pore dimensions. This uniformity provides a test of our interpretation of the number of processes required in the isotherm fits of the multiple equilibrium analysis, MEA. As expected from the two pores in the structure of HZSM-5, most adsorbates require two processes (K1,ads and K2,ads) to fit the adsorption isotherms. HZSM-5 is compared to amorphous carbonaceous adsorbents, revealing fundamental differences in their behavior. Small cylindrical channels in HZSM-5 lead to an unfavorable entropic contribution from restrictions imposed by adsorptive packing and inte...

New approach to sensitivity analysis of multiple equilibria in solutions

We consider multiple equilibria in solutions in which the interaction of n chemical species is described by means of m stoichiometrically independent reactions (SIRs). For the study of certain thermodynamic properties of such system. in particular, for sensitivity analysis, it is important to know the determinant Δ of the Hessian matrix of the Gibbs energy, as a function of the extent of the SIRs. Any linear combination of SIRs, in which (at least)m– 1 species are not involved, is called a Hessian response reaction (HR): Several properties of the HRs are pointed out, in particular, the equivalence of Δ to the sum of contributions origintaing from each HR. The effect of temperature and pressure on chemical equilibria in ideal solutions is analysed. It is shown that the sensitivity coefficient of a chemical species Ai may be presented as a sum of contributions coming from all HRs in which Ai is involved. Each of these contributions is a product of the stoichiometric coefficient of Ai, the enthalpy or volume change of the respective HR, and a concentration-dependent term which is always positive. It is also shown that the relaxation contribution to the heat capacity is a sum of contributions over all HRs.

Size distribution of small and large micelles. Multiple equilibrium analysis

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSize distribution of small and large micelles. Multiple equilibrium analysisPasupati MukerjeeCite this: J. Phys. Chem. 1972, 76, 4, 565–570Publication Date (Print):February 1, 1972Publication History Published online1 May 2002Published inissue 1 February 1972https://doi.org/10.1021/j100648a019RIGHTS & PERMISSIONSArticle Views920Altmetric-Citations230LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (699 KB) Get e-Alerts