Self-pulsations

We get a very similar time behavior in subharmonic generation where/1 = 0 and /2 / 0. Self-pulsation and multiperiodic evolution of intensities have been found. However, these findings are not investigated here. 

FIGURE 7 The modulation current (a) and the corresponding self-pulsation (b) of the lasing light output modulatedby a pulsed current with a current of I = 1.41. rd shows the delay time of the laser emission just after the supply of the pulsed current. 

Self-pulsations, i.e. periodic oscillations of the field intensity, appear as a result of a Hopf bifurcation of the stationary locked states. In terms of... 

We have noticed, that near the period-doubling bifurcation self pulsations appear, which are close to the diagonal in the space (01,02), cf. Fig. 6.9, orbit A. Such pulsations appear when there is no phase shift between the amplitudes oi and 02 of the lasers, cf. Fig. 6.9(A). On the contrary, near the Hopf bifurcation, we observe that self pulsations are close to the antidiagonal . Such a phenomenon was reported in Ref. [20] and called inverse synchronization . In this case, oi is shifted with respect to 02 by a half of the period, cf. Fig. 6.9(C). The orbit B in Fig. 6.9 corresponds to the intermediate regime. In the following two sections we consider these phenomena in more detail and show that the phase propagation parameter ip determines the possibility to observe identical or inverse amplitude synchronization. 

Solution (6.10) corresponds to a relatively small detuning. In this case, Aip converges to a constant for t —> oo, and the system settles on a stable CW solution. When the detuning 5 becomes larger 2rj, then Atp is the periodic function (considered modulo 27t) (6.11) with the period Tsyn = 2-kj. The growth rate of Api is determined by the term 2Tt[t /5 - Aif /2Tv i, i.e. the averaged frequency of self-pulsations is Afi = /5 — Arf. Note that their period tends to infinity as 5 —> 2 . 

H. Wenzel, U. Bandelow, H.J. Wiinsche, and J. Rehberg. Mechanisms of fast self pulsations in two-section DFB lasers. IEEE Journal of Quantum Electronics, QE-32 69-79, 1996. 

Antoine, C., Pimienta, V. Mass-spring model of a self-pulsating drop. Langmuir 29(48), 14935-14946 (2013)... 

In another paper Ya.B. considered2 the interaction between pressure pulsations in a powder-driven rocket chamber with supersonic flow of the combustion products and pulsations in the combustion velocity. It turned out that for small sizes of the combustion chamber self-generation of oscillations appears, leading to... 

Acoustic cavitation (AC), formation of pulsating cavities in a fluid, occurs when a powerful ultrasound is applied to a non-viscous fluid. The cavities are formed when the variable acoustic pressure in the rarefaction phase exceeds the cohesive strength of the fluid. Under acoustic treatment (AT), cavities grow to resonance dimensions conditioned by frequency, amplitude of oscillations, stiffness properties and external conditions, and start to pulsate synchronously (self-consistently) with acoustic pressure in the medium. The cavities undergo significant strains (compared to their dimensions) and their size decreases under compression up to collapsing. This nonlinear behavior determines the active, destructional character of the cavities near which significant shear velocities, local pressure and temperature bursts occur in the fluid. Cavitation determines the specific character of acoustic treatment of the fluid and effects upon objects resident in the fluid, as well as all consequences of these effects. 

The following equations will calculate Froude numbers for both the liquid and gas phases. The computer program will print out a message indicating whether the vertical pipe is self-venting, whether pulsating flow occurs, or whether no pressure gradient is required. 

The computer program PROG36 calculates the Froude numbers for the liquid and vapor phases. In addition, PROG36 will determine whether the pipe is self venting or whether pulsation flow is encountered. Table 3-13 shows the results for the 2-, 4-, and 6-inch (Schedule 40) pipes. Table 3-14 gives a typical input data and computer output for the 2-inch (Schedule 40) pipe. 

THIS PROGRAM WILL CALCULATE THE FROUDE NUMBERS OF VAPOR-LIQUID TWO-PHASE VERTICAL PIPE. IT FURTHER PRINTS OUT A MESSAGE IF THE PIPE IS SELF-VENTING, IF PULSATION FLOW OCCURS, OR IF NO PRESSURE GRADIENT IS NEEDED. 

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