Global velocity

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

It is also interesting to examine the global gas dynamic structure of upward propagating flames. Figure 3.1.6 gives an example of the global velocity field for the lean limit methane flame in the flame coordinates. The velocity distributions for all near limit flames studied share certain features. The central part of the bubble-shaped flame is... 

Global velocity distribution behind flame front. Upward propagation in 5.15% methane/air mixture, (a) vector map, (b) and (c) scalar maps of axial and radial velocity components, respectively. Spots are caused by condensation of water vapor on the glass walls. 

In general in complex media, the convection and diffusion of a solute is a difficult problem to analyze at the microscale and the moment method enables the analysis to be carried out at the macroscale leading to the replacement of the convective-diffusion problem by an effective global velocity and an effective dispersion tensor as in Eq. (4.6.30). Brenner s procedure analyzes the time evolution of the spatial moments (cf. Eq. 4.6.36) of the conditional probability density that a Brownian particle is located at a given position at a specific time knowing the position from which it was initially released into the fluid. 

A formulation removing both possible degeneracies has been introduced by [5]. This formulation has as its basic variables the wetting phase saturation and a so called global pressure p with values between pg and p . Furthermore, it introduces a global velocity. 

From the constitutive relationships, it is possible to derive relations between the pairs Pg,Pw, and p,s . For the expressions and a detailed introduction, see [11]. A drawback of this formulation is that boundary conditions now have to be given for global pressure and global velocity, which, being mathematical constructs rather than physical ones, are not directly available to physical measurements. 

The particle flux density, 7 ° , is due to the global velocity field of the solution given by... 

Zhao D, Lei J (2004) Seismic ray path variations in a 3D global velocity model. Phys Earth Planet Int 141 153-166... 

MAXEL, EIAXST ELEMENT COI mECTIVITY (MAXDF) NODAL VELOCITIES (MAXDF) GLOBAL LOAD VECTOR... 

The requirement of an accurate global energy surface is even more important for a quantum mechanical treatment than for the classical case, since the wave function depends on a finite part of the surface, not just a single point. The updating of the positions and velocities is computationally inexpensive in the classical case, once the... 

The numerical values of the transfer velocity K for the different gases are not well established. Its magnitude depends on such factors as wind speed, surface waves, bubbles and heat transfer. A globally averaged value of K often used for CO2 is about 10 cm/h. Transport at the sea-air interface is also discussed in Chapter 10 for a review see Liss (1983). 

Let us now consider the velocity autocorrelation function (VACF) obtained from the MCYL potential, (namely, with the inclusion of vibrations). Figure 3 shows the velocity autocorrelation function for the oxygen and hydrogen atoms calculated for a temperature of about 300 K. The global shape of the VACF for the oxygen is very similar to what was previously determined for the MCY model. Very notable are the fast oscillations for the hydrogens relative to the oxygen. 

Gas holdup and liquid circulation velocity are the most important parameters to determinate the conversion and selectivity of airlift reactors. Most of the reported works are focused on the global hydrodynamic behavior, while studies on the measurements of local parameters are much more limited [20]. In recent years, studies on the hydrodynamic behavior in ALRs have focused on local behaviors [20-23], such as the gas holdup, bubble size and bubble rise velocity. These studies give us a much better understanding on ALRs. 

By external stimulus at the plate electrode, migration of the ions in the solvent is induced, which changes the spatial concentration and so the local course of reactions [68]. By this means, weak electrical fields change the propagation velocity of the reaction zone through the capillary strong electrical fields ( supercritical ) further affect the global feature of the reaction in the capillary. 

The shear rate is computed locally using a global curve fit to the velocity profile. If AP/L is the pressure drop driving the flow across the pipe length L, the shear stress o(r) is expressed as... 

Here the CQ term represents the global effect due to nonuniform voids and velocity profiles. The VGU/(J) term represents the local relative velocity effect (Todreas and Kazimi, 1990). 

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