Periods oscillation

When looking at the snapshots in Figure A3.13.6 we see that the position of maximal probability oscillates back and forth along the stretching coordinate between the walls at = -20 and +25 pm, with an approximate period of 12 fs, which corresponds to the classical oscillation period r = 1 / v of a pendulum with... 

Place a high-frequency capacitor (ceramic or film) across the primary winding of the transformer, rectifier, or the element to be snubbed. Determine the capacitor value that produces an oscillation period which is three times the original period (Co). 

The difficulties arise from the enormous variation in time and length scales. They range from microscopic oscillation periods of the order... 

We have reviewed studies of the self-organized formation of ordered nanostructures by oscillatory electrodeposition. Although the mechanism is totally different in different cases and the structures of the resultant deposits vary greatly, they agree in that a unit structure is formed with one cycle of the oscillation. Periodic ordered... 

In general, if a particle is bound (E < 0) it will oscillate (classically) between some limits r = a, and r = b. For example, in an elliptic orbit of a hydrogen atom, the radius oscillates periodically between inner and outer limits. Only for a circular orbit is there no oscillation. Among the eigenvalues which have the same n, the one with lowest l has the largest amplitude in the vicinity of the nucleus. 

We emphasize the link with the name of the already formed class of kick-excited self-adaptive systems and phenomena the external force is linked, through the function e(x), with the motion coordinate in an adaptive mode, and at the same time it exerts action in the form of short impulses much shorter than the oscillation period of the system. 

Figure 12.3b shows the widths of the Bragg layers as a function of the layer number of the CBNL depicted in Fig. 12.3a. There are two notable properties of the Bragg layers (1) the width of the high-index layers is smaller than the width of the low-index layers, and (2) the width of the layers decreases exponentially as a function of the radius, converging asymptotically to a constant value. The first property exists in conventional DBRs as well and stems from the dependence of the spatial oscillation period, or the wavelength, on the index of refraction. The second property is unique to the cylindrical geometry and arises from the nonperiodic nature of the solutions of the wave equation (Bessel or Hankel functions) in this geometry.

The solution of these differential equations for [X] and [Y] indicate that the concentrations of intermediates of X and Y oscillate periodically with time. ... 

In period measurement a second crystal oscillator is essentially used as a reference oscillator that is not coated and usually oscillates at a much higher frequency than the monitor crystal. The reference oscillator generates small precision time intervals, with which the oscillation duration of the monitor crystal is determined. This is done by means of two pulse counters the first counts a fixed number of monitor oscillations m. The second is started simultaneously with the first and counts the oscillations of the reference crystal during m oscillations of the monitor crystal. Because the reference frequency F,. is known and stable, the time for m monitor oscillations can be determined accurately to 2/F,.. The monitor oscillation period is then... 

The field of oscillating reactions, or periodic reactions, or chemical clocks, came out of this background indeed quite a number of chemical systems have been described, which show this oscillating, periodic, regular behavior (Field, 1972 Briggs and Rauscher, 1973 Shakhashiri, 1985 Noyes, 1989 Pojman etal, 1994 Jimenez-Prieto etal., 1998). 

Equation (7.5) shows that the population of each eigenstate oscillates with its transition frequency as a function of r. For B transition of the iodine molecule that we will discuss later, the pump laser wavelength is 600 nm, which corresponds to the oscillation period of 2fs. If we require Ittx 1/10 stability for the relative phase between the two interfering WPs, attosecond stability is necessary for the delay t. The details of the experimental setup to prepare the phase-stabilized double pulses will be described in the following section [38, 39,47,48]. 

Figure 7.10 Wave packet interference observed with die ns probe pulse. The delay between the pump and control pulses was scanned around (a) 1.0 and (b) 1.5 The abscissa is converted into the relative phase of averaged oscillation period of y = 30—33 levels, (c) ns excitation spectra taken at fixed timings giving die phases tuned around a and shown in (a). Ref. is a reference data...

The time step Tstep = lOu determines each point in time starting from zero that the transient solver will calculate a solution. A safe estimation of the time step is an order of magnitude less than the period of a switching waveform. For example, the time step for a 100 kHz oscillator (period = 10 /xs) should be approximately 1 /xs. Tmax, the maximum time step, can be left out (at default) or specified to increase (decrease TMAX) or decrease (increase TMAX) simulation accuracy. This allows the simulator to take larger steps when the voltage levels in the circuit experience little change. A transient time domain analysis can prove to be the most difficult to get to converge. 

The oscillations of atmosphere fluctuation occur with a frequency in the order of 1 Hz, and the catalytic activities are greatly affected by the species of noble metals and exhaust gas conditions. Figure 4 shows the NOx conversion efficiency on a Pd catalyst as a function of oscillating periods and amplitudes in an engine test (Yokota et al., 1985). This figure indicates that there are suitable cycling conditions, which the catalytic activities are superior to that under the static condition, and the catalyst performance depends on the cycling... 

Fig. 4. NOx reduction behavior on Pd/alumina catalyst as a function of oscillation periods and amplitudes in an engine test. Engine 2L, l,600rpm and —440 Torr catalyst Pd 0.05g/L. A/F amplitude of oscillation 0.4(A), 0.7(0) and 1.0(D).

Fig. 6. Periodic operation effect on Pd/Al203 catalyst in CO-Oz reaction. Oscillation periods 0s( ), 1 s(3), 5s( ), 10 s(O) and 20 s(0). Periodic operation effect on Pd/Al203 catalyst in C0-02 reaction.

The intensity cross-correlation and XFROG trace of the optimal pulse contains three sub-pulses (Fig.3). The time separation between the sub-pulses almost matches 1.5 times the oscillation period of the first excited state (Tosc 440fs) [6]. 

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