In the rectangular coordinate system, one utilizes equations in which there are quadratic functions, in thepolar coordinate system, one utilizes equations in which there are trigonometric functions (that can be considered as infinite series).
A procedure is described which extends the applicability of the commonly used equations of state to the phase equilibria of the apolar-polar as well as strictly polar systems. The method defines a "residual activity coefficient" and uses it as a correction factor to the equilibrium K-values ...
Systems of equations appear in all types of real-world applications. A nice way to solve these equations is to use matrix operations like row...
A method of constructing Green's functions and matrices of mixed boundary value problems for regions bounded by coordinate lines in a rectangular Cartesian andpolarcoordinate systems (band, half-plane, rectangle, circle, ring, and circle and ring sectors) is presented. Several closed representations ...
As mentioned above the formulae are iterative processes meaning that a sequence of equations is calculated where the output is reentered into the same sequence of equations. The aim is to minimise the output value after a set number of iterations. For example, the Inverse Method outp...
Experimental vapor-liquid equilibria in the systems R 22-R 23, R 22-Co2, Cs2-R 22, R 23-Co2, Cs2-R 23 and their correlation by equations of state Vapor-liquid equilibria in systems with polar molecules tend to show a rather complex phase behavior. In order to investigate the phase boun...
The Direct Method computes the location of a point that is a given distance and azimuth from another point The Inverse Method computes the geographical distance and azimuth between two given points. As mentioned above the formulae are iterative processes meaning that a ...
The large enhancement in QSGW band gaps relative to the LDA is standard in polar compounds37. Nevertheless, within the random phase approximation (RPA), it has long been known that W is universally too large68,69, which is reflected in an underestimate of the static dielectric constant ϵ...
First order integrals of motion for Schr枚dinger equations with position dependent masses are classified. Eighteen classes of such equations with non-equiv... Hai Zhang® - 《Chinese Physics B》 被引量: 0发表: 2020年 On superintegrable systems with a position-dependent mass in polar-like coor...
The next model in our hierarchy is the Axisymmetric Horizon Dissolution (AHD) model, which solves the heat and reactive flow equations (Eqs. 1–8) as described in the Methods. In this setting a hot fluid flows through a thin horizon, dissolving it via the CHTF mechanism, eventually forming...