13 research outputs found
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 âproperly
transformed probability Euclidian vectorsâ that point on a manifold of
spherical symmetry. Furthermore, any macroscopic thermodynamic state âcloseâ to
equilibrium is described by a triplet that represent the âinfinitesimal volumeâ
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 âInverseâ 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 systemâs
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