First-order system least squares and the energetic variational approach for two-phase flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen–Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.     

Computing approximate Nash equilibria in general network revenue management games

Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

Solubility of carbon dioxide in aqueous solution of 2-amino-2-methyl-1-propanol and piperazine

In this work, new experimental results of the vapour-liquid equilibrium (VLE) of CO₂ in aqueous 2-amino-2-methyl-1-propanol (AMP) and piperazine (PZ) have been presented in the temperature range of 298-328 K and PZ concentration range of 2-8 mass%, keeping the total amine concentration in the solution at 30 mass%. The partial pressures of CO₂ were in the range of 0.1-1450 kPa. A thermodynamic model was developed to correlate and predict the VLE of CO₂ in aqueous AMP + PZ. The electrolyte nonrandom two liquid (ENRTL) theory has been used to develop the VLE model for the quaternary system (CO₂ + AMP + PZ + H₂O) to describe the equilibrium behaviour of the solution. The experimental data from this work and data available in the literature were used to regress the ENRTL interaction parameters. The model predictions are in good agreement with the experimental data of CO₂ solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, pH of the CO₂ loaded solution, and amine volatility.     

Liquid-crystal phase equilibria of Lennard-Jones chains

Liquid-crystal phase equilibria of Lennard-Jones chain fluids and the solubility of a Lennard-Jones gas in the coexisting phases are calculated from Monte Carlo simulations. Direct phase equilibria calculations are performed using an expanded formulation of the Gibbs ensemble. Monomer densities, order parameters, and equilibrium pressures are reported for the coexisting isotropic and nematic phases of: (1) linear Lennard-Jones chains, (2) a partially-flexible Lennard-Jones chain, and (3) a binary mixture of linear Lennard-Jones chains. The effect of chain length is determined by calculating the isotropic-nematic coexistence of linear Lennard-Jones chain fluids made of 8, 10, and 12 segments (8-, 10-, 12-mer). The effect of molecular flexibility on the isotropic-nematic equilibrium is studied for a Lennard-Jones 10-mer chain fluid with one freely-jointed segment at the end of the chain. An isotropic-nematic phase split and fractionation are reported for a binary mixture of linear 7-mer and 12-mer chains. Simulation results are compared with theoretical results as obtained from a recently developed analytical equation of state based on perturbation theory. Excellent agreement between theory and simulations is observed. The solubility of a monomer Lennard-Jones gas in the coexisting isotropic and nematic phases is estimated using the Widom test-particle insertion method. A linear relationship between solubility difference and density difference at isotropic-nematic coexistence is observed. It is shown that gas solubility is independent of the nematic ordering of the fluid, at constant temperature and density conditions.     

Measurement of water activities of alanine + tri-potassium citrate + water system at temperatures between 293.15 and 313 K—Experimental and modeling

Water activity measurements by isopiestic method have been carried out on the aqueous solutions of alanine + tri-potassium citrate (K₃Cit) over a range of temperatures at atmospheric pressure. From these measurements, values of the vapor pressure of solutions were determined. The effect of temperature on the vapor–liquid equilibrium of alanine + K₃Cit + H₂O systems has been studied. The experimental water activities have been correlated successfully with the segment-based local composition Wilson and NRTL models. The agreement between the correlations and the experimental data is good.     

Phase transitions for Belousov–Zhabotinsky reactions

The main objective of this article is to study the dynamic phase transitions associated with the spatial–temporal oscillations of the BZ reactions, given by Field, Körös and Noyes, also referred as the Oregonator. Two criteria are derived to determine (1) the existence of either multiple equilibria or spatiotemporal oscillations and (2) the types of transitions. These criteria gives a complete characterization of the dynamic transitions of the BZ systems from the homogeneous states. The analysis is carried out using a dynamic transition theory developed recently by the authors, which has been successfully applied to a number of problems in science. Copyright © 2011 John Wiley & Sons, Ltd.     

Formulation and computation of general financial equilibrium

In this paper a model of competitive financial equilibrium is introduced, which yields the optimal composition of assets and liabilities in each sector's portfolio, as well as the market clearing prices for each instrument. The variational inequality formulation of the equilibrium conditions is then utilized to establish existence and uniqueness properties of the solution pattern. Finally, an algorithm is proposed for the computation of the equilibrium pattern; the algorithm resolves the problem into simple network subproblems which can then be solved in closed form. The algorithm is then applied to an example.