Vector circulation

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A vector flux through an area and vector circulation along a closed contour is the basic characteristic of a vector field in vector algebra. The apphcation of these concepts to an electrostatic field appears extremely fruitful. 

Fig. 11. Computer-simulated recirculating patterns in a mixing tank with full baffles (a) elevation view shows circulation patterns generated by turbine blades (b) plane view shows the effect of the baffle on the radial velocity vectors above the turbine blades.

The product withdrawal pipe is located in the annulus halfway up the draft tube where the vector of the circulation velocity of the suspension and that of the withdrawal velocity of the product point in the same direction. Using this arrangement ensures low particle classification effects. Furthermore, the feed tubes and withdrawal tube can be exactly positioned in the reactor and scaled... 

In turbulent flow there is a complex interconnected series of circulating or eddy currents in the fluid, generally increasing in scale and intensity with increase of distance from any boundary surface. If, for steady-state turbulent flow, the velocity is measured at any fixed point in the fluid, both its magnitude and direction will be found to vary in a random manner with time. This is because a random velocity component, attributable to the circulation of the fluid in the eddies, is superimposed on the steady state mean velocity. No net motion arises from the eddies and therefore their time average in any direction must be zero. The instantaneous magnitude and direction of velocity at any point is therefore the vector sum of the steady and fluctuating components. 

When DDT was widely used, it was released into the environment in a number of different ways. The spraying of crops, and the spraying of water surfaces and land to control insect vectors of diseases, were major sources of environmental contamination. Waterways were sometimes contaminated with effluents from factories where DDT was used. Sheep-dips containing DDT were discharged into water courses. Thus, it is not surprising that DDT residues became so widespread in the years after the war. It should also be remembered that, because of their stability, DDT residues can be circulated by air masses and ocean currents to reach remote parts of the globe. Very low levels have been detected even in Antarctic snow ... 

The use of recombinant viral vectors as vaccination tools displays considerable clinical promise. One potential complicating factor, however, centres around the possibility that previous recipient exposure to the virus being used as a vector would negate the therapeutic efficacy of the product. Such prior exposure would likely indicate the presence of circulating immune memory... 

The vector curl F is a measure of the vorticity of the field at P x, y, z) and is related to the net circulation integral per unit area around an element of area at P. 

The circulation of a vector field along a closed curve c is defined by the line integral... 

If Tz is interpreted as the z-component of a vector, the three-dimensional circulation integral per unit area defines the vector curl v. 

Since the gauge factor is in general dependent on the path and therefore not integrable, circulation vectors (compare 1.3.4) such as... 

Because tissue-specific vectors are aimed at increasing the influx of a drug into the target, assessment of unidirectional transport from the circulating plasma into the target organ is essential. In this context, integration plot analysis is a convenient in vivo method in which a tracer amount of vector is injected intravenously and the plasma (Cp) and tissue (Ct) con-... 

The principle is that, as energy is drawn from the vector potential and then contained and circulated in field form in a localized material region or path, the withdrawn -potential energy in space outside that localized path is continually... 

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