Direct dynamics straight

The methods presented next attempt to circumvent the laborious and painstaking fltting process in one way or another. These methods may all be called direct dynamics in that the dynamics calculations are based directly on the electronic structure data without the intermediary of a fit. The first of the methods (section 3.2) is called straight direct dynamics because it is an implementation of this approach in its purest and most straightforward form. 

One difficulty with straight direct dynamics is that the large number of electronic structure calculations required tends to mitigate against employing high levels of theory. Thus, for example, some direct dynamics calculations have employed minimum basis sets [32d] and semiempirical molecular orbital theory [7b]. 

The dynamics of the two-particle problem can be separated into center-of-mass motion and relative motion with the reduced mass /i = morn s/(rnp + me), of the two particles. The kinetic energy of the relative motion is a conserved quantity. The outcome of the elastic collision is described by the deflection angle of the trajectory, and this is the main quantity to be determined in the following. The deflection angle, X, gives the deviation from the incident straight line trajectory due to attractive and repulsive forces. Thus, x is the angle between the final and initial directions of the relative velocity vector for the two particles. 

Carpenter has coined the term dynamic matching to describe these direct nonstatistical trajectories. The motion and momentum of a system coming out of one TS region directs the system straight into a second TS, neglecting any nearby local... 

Other dynamic variables to be optimized include the direction of the liquid phase flow, combinations of static and dynamic cycles and use of straight or coiled tubes in the continuous manifold. 

The first term of the RHS of Eqs. 6.105a and 6.105b accounts for static, axial, molecular diffusion. In the case of a straight cylindrical tube, there is no tortuosity nor constriction, 7 = 1. There is no eddy diffusion either, nor any A term in Eqs. 6.105a, by contrast to Eq. 6.90a. This is expected in the case of a cylindrical open tube, where the flow is ideally laminar, with no local eddies. The second term in Eq. 6.105a accoxmts for the dynamic diffusion related to the nonhomogeneity of the gas phase in the radial direction, because of the Poiseuille radial flow profile. 

Similar results were found by Henry and Gilbert [33], who studied sulfur removal, nitrogen removal, and hydrocracking in small reactors. Most of the first-order plots were curved upward when LHSV was used, but straight lines were obtained with LHSV. The explanation proposed was that the reaction rate was directly proportional to the dynamic holdup, which was predicted to increase with following... 

According to the fluid dynamics, we can see that horizontally straight tube fluid for steady laminar flow (Zhai 2009). The tiny cylindrical fluid removed from an axis coincident with the tube axis, analysis the force in the horizontal direction (x direction) is shown in Lig. 4. 

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