Thermodynamic interpolation for the simulation of two-phase flow of non-ideal mixtures

This paper describes the development and application of a technique for the rapid interpolation of thermodynamic properties of mixtures for the purposes of simulating two-phase flow. The technique is based on adaptive inverse interpolation and can be applied to any Equation of State and multicomponent mixture. Following analysis of its accuracy, the method is coupled with a two-phase flow model, based on the homogeneous equilibrium mixture assumption, and applied to the simulation of flows of carbon dioxide (CO2) rich mixtures. This coupled flow model is used to simulate the experimental decompression of binary and quinternary mixtures. It is found that the predictions are in good agreement with the experimental data and that the interpolation approach provides a flexible, robust means of obtaining thermodynamic properties for use in flow models

On the Geometrical Representation of Classical Statistical Mechanics

In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by “properly transformed probability Euclidian vectors” that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state “close” to equilibrium is described by a triplet that represent the “infinitesimal volume” of the points, the Euclidian probability vector at equilibrium that points on a hypersphere of equilibrium thermodynamic state and a Euclidian vector a vector on the tangent bundle of the hypersphere. The necessary and sufficient condition for such representation is expressed as an invertibility condition on the proposed transformation. Finally, the relation of the proposed geometric representation, to similar approaches introduced under the context of differential geometry, information geometry, and finally the Ruppeiner and the Weinhold geometries, is discussed. It turns out that in the case of thermodynamic equilibrium, the proposed representation can be considered as a Gauss map of a parametric representation of statistical mechanics

Statistical Inference of Rate Constants in Chemical and Biochemical Reaction Networks Using an “Inverse” Event-Driven Kinetic Monte Carlo Method

The use of rate models for networks of stochastic reactions is frequently used to comprehend the macroscopically observed dynamic properties of finite size reactive systems as well as their relationship to the underlying molecular events. Τhis particular approach usually stumbles on parameter derivation associated with stochastic kinetics, a quite demanding procedure. The present study incorporates a novel algorithm, which infers kinetic parameters from the system’s time evolution, manifested as changes in molecular species populations. The proposed methodology reconstructs distributions required to infer kinetic parameters of a stochastic process pertaining to either a simulation or experimental data. The suggested approach accurately replicates rate constants of the stochastic reaction networks, which have evolved over time by event-driven Monte Carlo (MC) simulations using the Gillespie algorithm. Furthermore, our approach has been successfully used to estimate rate constants of association and dissociation events between molecular species developing during molecular dynamics (MD) simulations. We certainly believe that our method will be remarkably helpful for considering the macroscopic characteristic molecular roots related to stochastic physical and biological processes