Velocity class

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

Theoretical level populations. Sinee there are population variations on time seale shorter than some level lifetimes, a complete description of the excitation has been modeled solving optical Bloch equations Beacon model, Bellenger, 2002) at CEA. The model has been compared with a laboratory experiment set up at CEA/Saclay (Eig. 21). The reasonable discrepancy when both beams at 589 and 569 nm are phase modulated is very likely to spectral jitter, which is not modeled velocity classes of Na atoms excited at the intermediate level cannot be excited to the uppermost level because the spectral profile of the 569 nm beam does not match the peaks of that of the 589 nm beam. 

To see more fringes we have to increase the coherence length and therefore decrease the velocity spread. For this purpose we employ a mechanical velocity selector, as shown after the oven in Fig. 1. It consists of four slotted disks that rotate around a common axis. The first disk chops the fullerene beam. Only those molecules are transmitted which traverse the distance from one disk to the next in the same time that the disks rotate from one open slot to the next. Although two disks would suffice for this purpose, the additional disks decrease the velocity spread even further and help to eliminate velocity sidebands. By varying the rotation frequency of the selector, the desired velocity class of the transmitted molecules can be adjusted. To measure the time of flight distribution we chopped the fullerene beam with the chopper right behind the source (see Fig. 1). The selection is of course accompanied by a significant loss in count rate, but we can still retain about 7% of the unselected molecules. 

Fig. 10 - Velocity classes in interaction with the Laser beams at...

In fact the interaction frequency is not defined with an infinite precision the interaction has some width on the frequency scale, which is the natural width Aoyj = 1/x (inverse of the lifetime). To this natural width Ao)n corresponds, on the velocity scale, some interval Ay = Aw /k. All the atoms belonging to this interval constitute the velocity class interacting with the Laser beam propagating in the forward direction (z positive). 

The principle of saturation spectroscopy derives immediately from the foregoing when the Laser frequency is different from the transition frequency wi, the two waves, forward and backward, interact with different atoms, belonging to two different velocity classes. On... 

One curve of weak intensity, a broad Gaussian curve (with Doppler width Awp), which corresponds to the absorption of two photons propagating in the same direction backward or forward by two symmetrical velocity classes (+ V2 or - V2). 

Assume that for the center frequencies coi and co2 of the two transitions coi — C02I < Acod holds. At the laser frequency co = (coi + ct>2)/2, the incident wave is shifted against coi by Aco = co — coi = (co2 — < i)/2. If it saturates the velocity class (Vz dvz) = (co2 — (0 )l2k zb yk on the transition 1 with center frequency co, it is in resonance with molecules in this subgroup. Since the reflected wave experiences the opposite Doppler shift, when it saturates the same velocity class it is in resonance with molecules in the same subgroup in transition 2 with the center... 

Estimates of landslide velocities have been made by repeated surveys of the positions of displaced objects (Thomson Hayley 1975), by reconstruction of the trajectories of portions of the displaced mass (McConnell Brock 1904) by eyewitness observations (Tavenas et al., 1971) and by instrumentation (Mikkelson 1996). Estimates of largest velocities of substantial portions of the masses displaced in landslides give guidance about likely impacts of landslides. Rates of movement within a landslide differ with position, elapsed time and the time interval over which the rate is estimated such differences argue against precise reports of landslide velocity. The velocity classes can however be correlated with observed consequences (lUGS/ WG 1995, Table 2). 

The inherent resolution of collinear-beam spectroscopy is still limited by the residual Doppler broadening. In beams with a broad velocity distribution the labeling of one velocity class by optical pumping, probed in a second Doppler-tuning zone, was exploited already before narrow Doppler widths were achieved. The complete elimination of the first-order Doppler effect in resonant two-photon absorption on Ne I has been discussed in Section 3.3, in connection with a precision measurement of the relativistic Doppler effect. A similar experiment was performed on In I, where the 29p Rydberg state was excited from 5p Pi/2 via 6s Si/2 and detected by field ionization. The linewidth caused by the laser jitter can be reduced to the transit-time limit of a few hundred kilohertz. 

Classical saturated absorption experiments on fast beams require different laser wavelengths to saturate and probe the same transition. However, a three-level system in V or A configuration can be realized to use the same direct and retroreflected laser beam interacting with the velocity class p under the condition... 

For the discussion of the chaotic behavior statistical methods will be used. The relative cumulative frequency or the probability, respectively, is shown in Figure 7 for four velocity classes, see Table 3. From these data the relative frequency or probability density, respectively, is obtained, see Figure 8. It turns out that the frequency distribution is completely non-Gaussian, and the range characterizing the statistical dispersion is increasing with the relative velocity of the impact, while midrange point and mean value coincide fairly well, see Table 4. 

Assume that for the center frequencies Wj and W2 of the two transitions wj-W2 < Awjj holds. At the laser frequency w = (wj+o 2)/2 the incident wave saturates the velocity class (v ldv ) = u>2-w /2k 7k on the transition 1 with center frequency Wj while the reflected wave saturates the same velocity class on the transition 2 with the center frequency a>2- therefore observes, besides the saturation signals at Wj and W2 (where the velocity class Vg = 0 is saturated), an additional saturation signal (cross over) at w = i(wj+W2) because one of the two waves causes a decrease -ANj of the population density in the common lower level or an increase +AN2 in the common upper level, which is probed by the second wave on another tran-... 

Suspended particle transport is the result of dynamic equilibrium between particle detachment and deposition (sedimentation). A suspended particle will settle when the fluid shear stress drops below a critical level. Neglecting reaction, mass conservation of an insecticide associated with particles in settling velocity class i can be described by ... 

The velocity of a fast accelerated atom is typically 1 mm/ns compared to an average thermal velocity of lO mm/s. Thus the kinematics becomes important the first-order Doppler shift can be as large as 100 A and the second-order shift several GHz. Thus resonant three-level spectroscopy, using only one laser field can be carried out by Doppler tuning the energy levels appropriate. A simplified three-level system is shown in Fig.2. The excited velocity classes determined by... 

A doublet structure, which is extremely velocity (energy) dependent, is found. It only manifests itself for velocity classes corresponding to the power broadened homogeneous linewidth of the TPA. In the present case this corresponds to an energy variation of 1 V around the resonant energy E. Thus we have established a method to identify and locate the exact resonant three-level con-... 

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