Low-frequency instabilities

These findings validate the approach of Krier et al. (53) when they adopted the collapsed A/PA—GDF model to predict low frequency instability behavior of composite solid propellants at normal rocket pressure. Since m = 1.5 X 10 5 sec. at these pressures, their quasi-steady treatment of the O/F flame reaction time is valid for low freqeuncies above about 5000 c.p.s., the dynamic lag of the O/F flame must be taken into account—the dynamic lag of the A/PA flame need be considered only when frequencies approach 100 k.c.p.s. 

R. Akiba and M. Tanno, Low Frequency Instability in Solid Rocket Motors, in Proceedings of the First Symposium International) on Rockets and Astronautics, Yokendo, Bunkyo-Ku, Tokyo (1959), 74-82. 

Low-frequency instabilities, about 5 to 10 times slower than the frequency of screw rotation... 

The higher-frequency components of the current waveform also do not contribute to the steady-state torque. They do, however, increase the total RMS current resulting in added IR (I, current R, resistance) losses in the stator winding. In addition to higher-frequency current components there can also be low-frequency instabilities in the currents seen by the AC motors on variable-frequency controllers. These asynchronous components of current again cause added losses without contributing to the steady-state torque production. Motor designs that help minimize harmonic currents lead to low IK losses. 

Pressure drop oscillations (Maulbetsch and Griffith, 1965) is the name given the instability mode in which Ledinegg-type stability and a compressible volume in the boiling system interact to produce a fairly low-frequency (0.1 Hz) oscillation. Although this instability is normally not a problem in modern BWRs, care frequently must be exercised to avoid its occurrence in natural-circulation loops or in downflow channels. 

To reduce spurious signals due to drifts of the EPR line setting arising from mechanical and thermal instabilities, double coding of the ENDOR information is often employed23). Normally a low-frequency Zeeman modulation (30-300 Hz) is applied while the rf field is frequency or amplitude modulated at frequencies of about 1-30 kHz. This modulation scheme, however, has two major disadvantages ... 

Peskin and Raco (P3) have given a theoretical analysis of both ultrasonic and electrostatic atomization from the point of view of liquid instability. They conclude that atomization with low frequency ac will require about twice the field strength as dc but that, by going to high frequency, lower fields are possible with conducting liquids. The value for the critical field for atomization given by these authors for a dc field is, however, smaller than that which would be calculated from Eq. (39) by a factor of (1/32)1/2. This presumably reflects the simplified one-dimensional model used in their derivation. 

When an energetic material burns in a combustion chamber fitted with an exhaust nozzle for the combustion gas, oscillatory combustion occurs. The observed frequency of this oscillation varies widely from low frequencies below 10 Hz to high frequencies above 10 kHz. The frequency is dependent not only on the physical and chemical properties of the energetic material, but also on its size and shape. There have been numerous theoretical and experimental studies on the combustion instability of rocket motors. Experimental methods for measuring the nature of combustion instability have been developed and verified. However, the nature of combustion instability has not yet been fully understood because of the complex interactions between the combustion wave of propellant burning and the mode of acoustic waves. 

Instabilities caused by the anisotropy of conductivity and corresponding to a periodic deformation of the alignment of the director in a nematic monodomain under the action of a direct current or low-frequency alternating current. 

There is a possibility that concern over the new feedback loop and system instability has overshadowed the improvement in potentiostatic control when F = 1. This change is not readily apparent in the graphs, but the low-frequency, long-time value of Eg/Vj is unity in the presence of faradaic current. After the instability is cured, the dependence of potential on current will be more evident than it is now. 

Electric fields may interact with flows fed by hydrostatic or pumping action [91]. Flows driven by electroosmotic means may be mixed as well by the action of fluctuating electric fields, which creates oscillating electroosmotic flows and has been termed electrokinetic instability (EKI) [25, 93], In this way, rapid stretching and folding of material lines are induced, not unlike the effect of stirring. In one realized example, comparatively low frequencies, below -100 Hz, and electric field strengths in excess of 100 V mm1 are applied for channels with dimensions of about 50 pm [25],... 

The perovskite structure is, of course, of special significance in the electroceramics context since the ferroelectric perovskites are dominant in the ceramic capacitor, PTC thermistor and electromechanical transducer industries. The structure favours the existence of soft modes (low frequency phonons) as evidenced by its tendency to instability, for example the ferroelectric-paraelectric transition. Instability is evident in the case of the T23 compound which exhibits a tetragonal-orthorhombic transition in the region of 700 °C (the exact temperature depends on the oxygen content). Extensive twinning, very reminiscent of ferroelectric domain structures, is observed. 

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