Normal component

The first equation (1) is the equation of state and the second equation (2) is derived from the measurement process. Finally, G5 (r,r ) is a row-vector that takes the three components of the anomalous ciurent density vector Je (r) = induced magnetic field. This system is non hnear (bilinear) because the product of the two unknowns /(r) and E(r) is present. 

In Fig. 2a, we compare the modulus of the normal component of the magnetic induction B (r) provided by the sensor and the one calculated by the model. Because of the excitation s shape, the magnetic induction B° (r) is rotation invariant. So, we only represent the field along a radii. It s obvious that the sensor does not give only the normal component B = but probably provides a combination, may be linear, of... 

The normal component of velocity and tangential component of surface force are set to zero along a line of symmetry. For the domain shown in Figure 3.3 these are expressed as... 

The probability is normalized, since Eq. (1-44) was assembled from separately normalized components. 

Here is a normal component of the boundary displacements vector u defined by the decomposition... 

Given W G we have q = —aijn n > 0, and hence, the density q is defined by the normal component of the surface forces at At the end, in Section 2.8.3, we establish the stability of solutions with respect to perturbations in the crack shape. 

There is assumed to be no interaction between the superfluid and normal components, thus the superfluid component can diffuse very rapidly to a heat source where it absorbs energy by reverting to the normal state. It thereby produces the very high effective thermal conductivity observed in helium II. 

Suppose now that the force acted not normal to the face but at an angle to it, as shown in Fig. 3.1(b). We can resolve the force into two components, one, F(, normal to the face and the other, F, parallel to it. The normal component creates a tensile stress in the block. Its magnitude, as before, is F, /A. 

Here n is the unit vector perpendicular to the surface S and directed outward, and Tn the normal component of an arbitrary vector X, which is a continuous function within volume V. As was pointed out, Equation (1.67) has an infinite number of solutions let us choose any pair of them, U p) and U2(p), and form their difference ... 

The normal component of the attraction field due to planar surface masses... 

Fig. 1.13. (a) Thin layer and surface mass, (b) normal component of the field due to surface masses, (c) illustration of a solid angle near surface, (d) normal component along profiles 1, 2, and 3. 

At every point above and beneath the masses, the field can be represented as a sum of the tangential and normal components of the field ... 

Further we assume that the masses are distributed uniformly that is, a — constant. Applying the principle of superposition we obtain for the normal component of the field due to all surface masses ... 

Now we will describe the behavior of the normal component in several cases. 

Case three A plane surface has a form of a disk with radius a The normal component of the field at points of the z-axis is... 

One more feature of the field behavior is worth noting. Inasmuch as the layer has infinite extension in horizontal planes, the distribution of masses possesses axial symmetry with respect to any line parallel to the z-axis that passes through the observation point. For this reason, it is always possible to find two elementary masses such that the tangential component of the field caused by them is equal to zero. Respectively, the field due to all masses of the layer has only a normal component gz. 

One can say that we have expressed the disturbing potential in terms of an unknown density. Now we demonstrate that this transition is justified because it is possible to obtain the integral equation with respect to a. In Chapter 1, it was shown that the discontinuity of the normal components of the field at both sides of the surface masses is equal to —2nka. Correspondingly, we have... 

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