The amount of resin existing in crude oil highly affects the asphaltene precipitation values and results in formation of precipitation, asphaltene and resin and also pressure and temperature variations in such reservoirs. According to the literature, the effect of resin content has not been studied. The equation of state (AEOS) is one of the most applicable models which was also used in this study. The compressibility factor was assumed to be made of physical and chemical components. SRK equation of state was used in physical component. Considering the fact that asphaltene and resin do not interact in gas phase and that asphaltene and resin precipitations are in liquid state, vapor-liquid and liquid- liquid equilibrium calculations were applied. Asphaltene precipitation values were calculated from simulations the results were then compared to experimental data. Finally the resin precipitation values were measured.

In this research the one dimensional two-phase flow equqtion for the simultaneous flow of air and water from a vertical soil column presented here based on the aljebraic sum of the water and air velocities (the total velocity) which have been derived elsewhere .In evaluating some of hydraulic parameters, the Brooks - Corey functions (Brooks and Corey 1964) are used. For the relative permeability and effective saturated to wetting and no wetting phases are used to calculated the parameters in this equation.To obtain hydraulic parameters in the Brooks and Corey equation, experimental investigation presented and hydraulic conductivity is measured and the same column homogeneous soil is dryed.The experimental data is companied with the predicted values by this equation, which was showed a good agreement.On the other hand the values of D* and a are culculated by the Brooks - Corey functions and the results of the changes of these parameters over the conclusions were evaluated and it shoued that the D* changes had a significant or meaningful effect on the computations but the changes of a had not a considerable effect on the computations so, we can consider its quantity as (1) because its practical objects. Concerning to the complicated connection of quantities the volume of computations is reduced considerably.

In this paper, the general Riccati differential equation is solved by using the Adomian’s decomposition method (ADM), modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), homotopy perturbation method (HPM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. A numerical example is studied to demonstrate the accuracy of the presented methods.

In this paper we review several kinds of Chaplygin gas as a model of dark energy and introduce developed Chaplygin gas which is unification of all previous models. Dark energy considered as fluid of many body system with specific equation of state. We show, as a main goal of this paper that developed Chaplygin gas equation of state can be obtained from string theory like ordinary Chaplygin gas equation of state. We write string Hamiltonian and obtain equation of motion. Then compare it with Euler equation in fluid mechanics which yields to a differential equation. Solving this differential equation give us developed Chaplygin gas equation of state.

On one hand a two-level atom is utilized as a qubit in quantum information technology and on the other hand the light in quantum optics is usually in the squeezed state. These reasons motivated us to explore the dynamic of a two-level atom which is driven by a field in the squeezed state. To this goal, the atom operators and the Heisenberg-Langevin equation have been employed. The master equation which reveals the dynamic of the atom has been derived using some features of the squeezed state and doing some algebra. Finally, the dynamic of the two-level atom which is driven by squeezed state field has been simulated by the derived master equation. Also, the effect of atom parameters on the dynamic has been investigated.