Round-trip time

The tilt indetermination The round trip time of light to the mesosphere is 0.6 ms (at zenith). It is significantly shorter than the coher-... 

In order to remove the perturbation h t) from the integral we supposed that the period of the gravitational wave was much longer than the round trip time of light). The observer now concludes that the spatial distance Lg between the two mirrors is ... 

A simple Michelson interferometer. If we place two mirrors at the end of two orthogonal arms of length L oriented along the x and y directions, a beamsplitter plate at the origin of our coordinate system and send photons in both arms trough the beamsplitter. Photons that were sent simultaneously will return on the beamsplitter with a time delay which will depend on which arm they propagated in. The round trip time difference, measured at the beamsplitter location, between photons that went in the a -arm (a -beam) and photons that went in the y arm (y-beam) is... 

The superposition principle allows us to assume just a single scatterer in the view of the radar. The transmitted signal hits this scatterer whose distance (we measure distance and time in the same units) from the (collocated) transmitter and receiver is r. Assume that the scatterer is stationary. The return signal will be a delayed version of the original, delayed by the total round trip time from the radar to the scatterer. Specifically the signal voltage at the antenna of the receiver is... 

FIGURE 7.4 Only the velocity component perpendicular to a wall contributes to the pressure, since other components do not change the round-trip time. 

Intermolecular collisions do not cause large deviations from the ideal gas law at STP for molecules such as N2 or He, which are well above their boiling points, but they do dramatically decrease the average distance molecules travel to a number which is far less than would be predicted from the average molecular speed. Collisions randomize the velocity vector many times in the nominal round trip time, leading to diffusional effects as discussed in Chapter 4. If all of the molecules start at time t = 0 at the position x = 0, the concentration distribution C(x,t) at later times is a Gaussian ... 

In this case the electric field would be repetitive with the round trip time. Therefore C(t) is a constant and its Fourier transform is a delta function centered as uc = 0. If it becomes possible to build a laser able to produce a stable pulse train of that kind, all the comb frequencies would become exact harmonics of the pulse repetition rate. Obviously, this would be an ideal situation for optical frequency metrology. 

The output is thus a continuous train of pulses separated by the dye cavity round-trip time. Even though the pump laser pulses may be of the order of 200 ps long, dye laser pulses of less than 10 ps can be achieved by synchronous pumping. This is because the dye molecules have extremely large stimulated emission cross-sections and the dye laser pulse passing through the dye stream immediately de-excites the dye molecule, in a few picoseconds, by stimulated emission [13]. 

Since the round-trip times of the classical periodic orbits scale according to 1/1 1, a change of variables to lly/ E shows that the Fourier... 

These vesicles, containing LDL, subsequently fuse with lysosomes, acidic vesicles that carry a wide array of degradative enzymes. The protein component of the LDL is hydrolyzed to free amino acids. The cholesteryl esters in the LDL are hydrolyzed by a lysosomal acid lipase. The LDL receptor itself usually returns unscathed to the plasma membrane. The round-trip time for a receptor is about 10 minutes in its lifetime of about a day, it may bring many LDL particles into the cell. 

Where L is the cavity length and c is the velocity of light the Tp parameter is the cavity round-trip time. The width of the pulse (FWHM) is given approximately by... 

The derivative df /dE can be determined by a linear regression, where the number of regression points is flexible. Initial batches with the limited statistics of only a few round trips may require a larger number of regression points than subsequent batches with smaller round-trip times and better statistics. 

The scaling of round-trip times is shown in Fig. 3 for the two-dimensional fully frustrated Ising model. The power-law slowdown of round-trip times for the flat-histogram ensemble is reduced to a logarithmic correction... 

Fig. 3. Scaling of round-trip times for a random walk in energy space sampling a flat histogram open squares) and the optimized histogram solid circles) for the two-dimensional fully frustrated Ising model. While for the multicanonical simulation a power-law slowdown of the round-trip times 0 N L ) is observed, the round-trip times for the optimized ensemble scale like 0([A ln A ] ) thereby approaching the ideal 0(A )-scaling of an unbiased Markovian random walk up to a logarithmic correction...

Let i/(t) be the total execution time of a Web Service (including the round trip time of the communication) measured at the current time t, or another varying parameter of Web Services that we use for selection. A monitor logs the values y To), y To + S), y TQ + 2d), etc., where tq is the first measured value and 6 is an elementary time slot, which is always equal to one in case of a logical clock. Subsequently, envelopes for the measured values (e.g. maximum execution time envelopes) are computed for the last M blocks of duration T6. They describe the dynamics from short-term fluctuations (Wi) to long-term trends flYr) where i = 1... M and k = 1... T ... 

Thus, the total horizontal round-trip time is ... 

The presence of the AO modulator within the laser cavity causes a loss of energy at times other than the round-trip time for the photons and the nulls In the AO crystal. If the cavity length matches the AO crystal frequency, then the photons accumulate in a single bunch and bounce back and forth together within the laser cavity. This is the mode-locked condition. 

The time delay between successive transmitted pulses equals the cavity round-trip time Tr = 2L/c. The nth pulse therefore is detected at the time t = 2 L/c. If the time constant of the detector is large compared to Pr, the detector averages over subsequent pulses and the detected signals give the exponential function... 

If the modulator is placed inside the laser resonator with the mirror separation d and the mode frequencies = vo m cjld (m = 0,1,2,...), the sidebands coincide with resonator mode frequencies if the modulation frequency / equals the mode separation Av = cjld. The sidebands can then reach the oscillation threshold and participate in the laser oscillation. Since they pass the intracavity modulator they are also modulated and new sidebands y = vq i 2/ are generated. This continues until all modes inside the gain profile participate in the laser oscillation. There is, however, an important difference from normal multimode operation the modes do not oscillate independently, but are phase-coupled by the modulator. At a certain time the amplitudes of all modes have their maximum at the location of the modulator and this situation is repeated after each cavity round-trip time T = 2d c (Fig. 6.8c). We will discuss this in more detail The modulator has the time-dependent transmission... 

The optimum gain for the dye-laser pulses is achieved if they arrive in the active medium (dye jet) at the time of maximum inversion AN(t) (Fig. 6.15). If the optical cavity length d2 of the dye laser is properly matched to the length d of the pump laser resonator, the round-trip times of the pulses in both lasers become equal and the arrival times of the two pulses in the amplifying dye jet are synchro-... 

A KC1 T1° color-center laser with end mirrors MO and Ml is synchronously pumped by a mode-locked Nd YAG laser. The output pulses of the color-center laser at X = 1.5 nm pass the beam splitter S. A fraction of the intensity is reflected by S and is focused into an optical fiber where the pulses propagate as solitons, because the dispersion of the fiber at 1.5 pm is dn/dX > 0. The pulses are compressed, are reflected by M5, pass the fiber again, and are coupled back into the laser resonator. If the length of the fiber is adjusted properly, the transit time along the path M0-S-M5-S-M0 just equals the round-trip time T = 2d c through the laser resonator MO-Ml-MO. In this case compressed pulses are always injected into the laser resonator at the proper times t = - - qld / c q = 1,2,...) io superimpose the... 

Control loop tuning was another important aspect that needed to be addressed to make the system widely applicable without requiring extensive testing or expertise on the part of the user, in particular, the dynamic characteristics of the process as seen by the measurement system depend upon the number of cycles between measurements, which is determined by the round trip time of the TCS. This depends upon the number of measurements made within a round trip, and therefore on the number of cavities and sections, which is both job and machine dependent To address this issue, an analytical method was developed and implemented to compute controller gains explicitly accounting for the actual TCS round trip time. 

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