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The SAFT equation of state was developed using statistical mechanical methods (in particular the perturbation theory of Wertheim [28]) to describe the interactions between molecules in a system. [20] [29] [30] The idea of a SAFT equation of state was first proposed by Chapman et al. in 1988 and 1989.
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. In statistical mechanics applications prior to the introduction of the Metropolis algorithm, the method consisted of generating a large number of random configurations of the system, computing the properties of interest (such as energy or density) for each configuration ...
The equation of state may be used in Friedmann–Lemaître–Robertson–Walker (FLRW) equations to describe the evolution of an isotropic universe filled with a perfect fluid. If a {\displaystyle a} is the scale factor then ρ ∝ a − 3 ( 1 + w ) . {\displaystyle \rho \propto a^{-3(1+w)}.}
The Benedict–Webb–Rubin equation (BWR), named after Manson Benedict, G. B. Webb, and L. C. Rubin, is an equation of state used in fluid dynamics.Working at the research laboratory of the M. W. Kellogg Company, the three researchers rearranged the Beattie–Bridgeman equation of state and increased the number of experimentally determined constants to eight.
The Köhler equation relates the saturation ratio over an aqueous solution droplet of fixed dry mass to its wet diameter as: [4] = (), with: S {\displaystyle S} = saturation ratio over the droplet surface defined as S = p w / p w 0 {\textstyle S=p_{w}/p_{w}^{0}} , where p w {\textstyle p_{w}} is the water vapor pressure of the solution ...
This "law" is just a special case of dimensional analysis in which an equation containing 6 dimensional quantities, ,,,,, , and 3 independent dimensions, [p], [v], [T] (independent means that "none of the dimensions of these quantities can be represented as a product of powers of the dimensions of the remaining quantities", [45] and ...
The state-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation given by = + + (), with state vector x, control vector u, vector w of additive disturbances, and fixed matrices A, B, E can be solved by using either the classical method of solving linear differential equations or the Laplace transform method.
PC-SAFT (perturbed chain SAFT) is an equation of state that is based on statistical associating fluid theory (SAFT). Like other SAFT equations of state, it makes use of chain and association terms developed by Chapman, et al from perturbation theory. [1]