Uniformity parameter

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

In general the required performance criteria and product uniformity parameters stipulated in shotcrete specifications are as follows ... 

For a linear partial differential equation with relatively simple initial and boundary conditions, and uniform parameter values, an analytical solution may be obtained. Although simplified, analytical solutions can be put to a number of important uses. Analytical models may be used to [9] ... 

Assuming horizontal concentration gradients to be negligible, and further assuming uniform parameters in the vertical dimension, a mass balance for dissolved " Th or Th (Figure 1) can be written as... 

The second means of collecting multiple spectra involves collection from numerous locations within the vessel at one or more times. Multiple spectra drawn at one time from various locations in a blender may be compared to themselves or to spectra collected at different times, with similarity indicating content uniformity. Parameters for comparison can again include common statistical factors such as standard deviation, relative standard deviation, variance, a host of indices based on standard deviation, or the results from pattern recognition routines. Of course, spectra collected in this manner can also be compared to a library of spectra from previous homogenous blends. 

Figure 8.4 The order parameter R vs. the stirring rate shows the synchronization transition for different values of the non-uniformity parameter 6 (top). Phase diagram as a function of the stirring rate v and inhomogeneity S (bottom). The symbols represent synchronization, oscillator death and no synchronization (from Neufeld et al. (2003)).

Definition 1. Elements /i,..., fn G r (U, ox) with these properties are called uniformizing parameters in U. 

Multiplying by y/2, this becomes dy = xy3dx, so dx alone generates Ox/k-Therefore a is a uniformizing parameter everywhere on X and the projection p onto the rr-axis is etale ... 

It is clear that the general procedure used to derive the Navier-Stokes equations can be used to obtain the corrections to the hydrodynamic equations to higher order in the uniformity parameter. The order equations— the... 

The early studies on metal salts, including some chosen for their oxidizing ability, mostly used bacterial systems and, since no uniform parameter of activity was adopted, no real mechanistic pointers emerged from these... 

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