the srk two-parameter cubic equation of state has been used for the calculation of the equilibrium constant using the liquid and vapor fugacity coefficients for three binary mixtures. dew and bubble points have been determined using the equilibrium constants and the phase envelope has been plotted showing dearly that retrograde condenstaion occurs. the following percent deviations have been obt...

The present study investigates the use of different GE mixing rules in cubic equations of state for prediction of phase behavior of multicomponent hydrocarbon systems. To predict VLE data in multicomponent symmetric and asymmetric mixtures such as systems that contain light gases (nitrogen, carbon dioxide, etc.) and heavy hydrocarbons, the SRK equation of state has been combined with excess Gib...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

The transport properties of a fluid show complex dependence with temperature and pressure due to the combination different phenomena occurring at microscopic scale. entropy scaling concept aims describing this behavior by expressing reduced as one-variable functions Tv-residual entropy, thermodynamic quantity that can be straightforwardly estimated an equation state (EoS). In work, reformulated...

Abstract In this paper, different EOSs (Birch-Murnaghan, modified Lennard-Jones, Singh and Kao, Tait) are used to study the effect of high pressure on thermo-elastic properties nano TiO 2 (Nano titanium dioxide). The results V/V o variation calculations under pressure, using all four EOSs, showed excellent agreement with experimental data. This gives a conclusion that in bulk materials, Tait), ...

for primes p ≡ 1 (mod 3) up to 500, and found that Sp/(2√p) lay in the intervals [−1,− 12 ], (− 12 , 12 ), [ 1 2 , 1] with frequencies approximately in the ratio 1 : 2 : 3. He conjectured, somewhat hesitantly, that this might be true asymptotically. Kummer’s conjecture was disproved by Heath-Brown and Patterson [4]. In order to state their result we must introduce a little notation. Let ω = exp...

We study the null controllability of three parabolic equations. The control is acting only on one of the three equations. The three equations are coupled by means of two cubic nonlinearities. The linearized control system around 0 is not null controllable. However, using the cubic nonlinearities, we prove the (global) null controllability of the control system. The proof relies on the return me...