Uniform oscillator

The mathematical treatment of pulsing illumination has been described [Briers et al., 1926], After a number of cycles, the radical concentration oscillates uniformly with a constant radical concentration [M-] j at the end of each light period of duration t and a constant radical concentration [M-]2 at the end of each dark period of duration t = rt. The two radical concentrations are related by... 

Steady-state condition A condition occurring after all initial transient or fluctuating conditions have damped out in which currents, voltages, or helds remain essentially constant or oscillate uniformly without changes in characteristics such as ampHtude, frequency, or wave shape. 

We are primarily interested in phase characteristics of elements at the natural period of the loop. Assume, to begin, that a closed loop containing dead time is already oscillating uniformly. The input to the process is the sine wave... 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

Finally, the combustion zone does not always proceed at a uniform rate, but oscillates in time, slowing down and dren advancing rapidly. This effect is probably due to die non-uniform packing and distribution of die reactants in the compact. Also visual observation shows that the zone is not uniformly distributed around the periphety of the compact, and the observed movement of a hot spot around the periphery is usually refeiTed to as spin combustion. 

Nakanishi, S., Sakai, S., Nagai, T. and Nakato, Y. (2005) Macroscopically uniform nanoperiod alloy multilayers formed by coupling of electrodeposition with current oscillations. /. Phys. Chem. B, 109, 1750-1755. 

At x = 0, B(0) is equal to the uniform density of electrons. The first term of the right hand side makes a bulk peak around x = 0. It sharply damps outside, because the k-integration over the occupied states is similar in structure to the following damping oscillation function ... 

Finally, we can also find in the literature arrangements where the working electrode is also the emitter part of the transducer, normally named as sonotrode [22] or sonoelectrode [41]. Some authors have used only the main emitter surface as electrode [42], see Fig. 4.2b, and other authors have used the fully surface tip as working electrode [43], see Fig. 4.2c. In theory, this arrangement assures that all the specific effects derived from the ultrasound field propagation are directly focused on the surface electrode. Not only the shorted-lived bubbles non-uniformly collapse on the electrode surface but also the electrode surface itself oscillates. This provides additional effects which have been specifically used in the nanoparticles preparation. 

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