Stroboscopic

The layer width is taken from the relation d > 1,5 dg, where dg - thickness of a gas discharge gap. The employment of a resistive layer instead of electrode profiling can significantly simplify the device manufacture. The UV radiation is efficiently converted into a visible one by a number of photo-luminophors, e.g. Zn2Si04 Mn. For stroboscopic registration of fast-proceeding processes the luminophors with short period of luminescence are used, e.g anthracene etc. 

Use of stroboscopic techniques and carefully designed apparatus can make this sort of method very accurate. 

Any risk to occupants from stroboscopic effects of blade movements ... 

A convenient method for visualizing continuous trajectories is to construct an equivalent discrete-time mapping by a periodic stroboscopic sampling of points along a trajectory. One way of accomplishing this is by the so-called Poincare map (or surface-of-section) method (see figure 4.1). In general, an N — l)-dimensional surface-of-section 5 C F is chosen, and we consider the sequence of successive in-... 

Stroboscopic Method.—This method was developed a few years ago by the writer in collaboration with M. Schiffer, and is based on the transformation theory of differential equations.20 We shall give here only the heuristic approach to this method, referring for its analytical proof to other published material.21... 

One can interpret this physically as follows suppose that the trajectory of the harmonic oscillator be represented by a point on a rotating wheel. The eye observes a circle (the path of the point) if the wheel rotates rapidly this corresponds to continuous illumination. On the other hand, if one illuminates the rotating wheel with stroboscopic flashes separated by a period 2n, a given mark on the wheel appears as a fixed point. Thus, under continuous illumination one sees ... 

Since the phase of the flashes is arbitrary, the above statement holds for any radius and one can say that the limit cycle is a locus of fixed points for stroboscopic points approaching them from all directions both from inside and from outside. One can specify this condition by writing ... 

In our optical analogy, they permit calculating the stroboscopic point (pu9i) if one knows (p0,9>0) then (pz,[Pg.367]

If the process lasts long enough in comparison with the duration of the period 2v, one may consider (approximately) A , Ap, and A

difference equations (6-124) to the stroboscopic differential equations. 

The relation between the discontinuous procedure of Eqs. (6-124) and the continuous idealization of Eq. (6-126) is the same as that which exists between the sequence of discrete stroboscopic points and the pseudocontinuous motion of the point of the wheel which appears to the eye owing to the persistence of vision. 

In view of this, it is generally much simpler to treat the problem in terms of the stroboscopic differential equation than to attack it directly on the basis of the original differential equation (6-112). 

Examples of Application of the Stroboscopic Method.— We can consider two differential equations. 

Forming the second combination yx — xy, one obtains similarly the second stroboscopic differential equation... 

It is seen that now the stroboscopic system has a singular point defined by the relations23... 

One can also obtain the theory of synchronization by the stroboscopic method. If one starts with the differential equation... 

Omitting the intermediate calculations, the stroboscopic system in this case is... 

As the principal aim of the stroboscopic method is to obviate this difficulty by reducing the problem to the determination of stability of singular points, we include a brief statement of this approach. 

Setting p = A2 + B2 ift = arctan (AjB), and proceeding as we did previously (see Section 6.23) we obtain the first stroboscopic differential equation... 

It is necessary to show that the subharmonic resonance whose existence we have just ascertained is stable. Here the condition of stability is very simple, since in the stroboscopic method we deal with the stability of the singular point (and not of the stationary motion). 

L. Mandelstam and N. Papalexi performed an interesting experiment of this kind with an electrical oscillatory circuit. If one of the parameters (C or L) is made to oscillate with frequency 2/, the system becomes self-excited with frequency/ this is due to the fact that there are always small residual charges in the condenser, which are sufficient to produce the cumulative phenomenon of self-excitation. It was found that in the case of a linear oscillatory circuit the voltage builds up beyond any limit until the insulation is ultimately punctured if, however, the system is nonlinear, the amplitude reaches a stable stationary value and oscillation acquires a periodic character. In Section 6.23 these two cases are represented by the differential equations (6-126) and (6-127) and the explanation is given in terms of their integration by the stroboscopic method. 

If one proceeds as indicated in Section 6.23, one obtains the stroboscopic system... 

A classic self-light stroboscopic image of a premixed flame undergoing a tulip inversion in a closed tube. There is an interval of 4.1 ms between the images of a water vapor saturated CO/Oj flame arranged to have a flame speed comparable with that of a stoichiometric methane/air flame. The tube is 2.5 cm in diameter and 20.3 cm long. (Adapted from Ellis, O.C. de C. and Wheeler, R.V., /. Chem. Soc., 2,3215,1928.)... 

Stroboscopic schlieren record of the DDT process with onset at flame front in 2H2 + Oj initially at a pressure of 0.073 MPa. (From Urtiew, P. A. and Oppenheim, A.K., Proc. R. Soc. A, 295,13,1966. With permission)... 

In the 1960s, Oppenheim et al. [10,19,20] succeeded in obtaining photographs with better resolution by means of schlieren technique with microsecond flash and then with the very short (less than 10 s) laser light pulses. This facilitated the attainment of a stroboscopic set of essentially still photographs that revealed many details of DDT. At the same time, Soloukhin [21] published a series of streak photographs taken with schlieren system and Denisov and Troshin [22] discovered that detonation leaves a record of its passage in the form of imprint on a wall coated with the thin layer of soot. 

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