Phase perturbation

Subject to phase perturbations unless otherwise noted. 

The interaction matrix can be built following Le Louam and Tallon, 2002. We assume narrow fields approximation for the propagation from the turbulent layers, i.e. phase perturbations by the turbulent layers simply add at the level of the pupil. It also means that scintillation is negligible. A point x, y) in the turbulent layer at altitude h is projected onto the pupil at (rcpupii, 2/pupii) ... 

In a CPA, because a large secondary dispersion is added to the stretcher, the spectrum is mapped to the temporal waveform in the amplifier. For that reason, the phase change added to the pulse shaper cannot cause a large change in the pulse shape in the CPA. Self-phase modulation depends on the temporal amplitude transition. Therefore, the phase perturbation can be regarded as almost linear in the amplifier. Thus, the inverse of the spectrum phase difference between the acquired and the target phase is added to the pulse shaper. 

In this wide-beam simulation, the initial condition is a Gaussian pulse with a phase perturbation. The waist of the initially collimated Gaussian was chosen to be 5 mm, the pulse duration is 500 fs, A = 248 nm, and the maximal intensity is 2 x 1014Wm-2. The total pulse energy is approximately 9mJ. A random phase perturbation is imposed on the pulse to initiate the transverse break-up of the pulse into multiple filaments (see Fig 13.3). We adjusted the amplitude of the perturbation such that it results in the filamentation onset after a few meters of propagation. 

Figure 4.29 Perturbation signals recorded on a four-compound plateau. Top, experimental results. Bottom signal calculated with the equilibrium-dispersive model and the best coefficients of a competitive quaternary bi-Langmuir isotherm. Compoxmds enantiomers of methyl- and ethyl-mandelate on a chiral phase. Perturbation as in Eq. 4.104 Reproduced with permission from J. Lindholm, P. Porssen, T. Fomstedt, Anal. Chem., 76 (2004) 5472 (Fig. 3). 2004, American Chemical Society.

System peaks arise when one or several components of the mobile phase are adsorbed on the stationary phase, and because their concentrations are such that their adsorption isotherms are not linear. Injection of the sample in the multicomponent mobile phase perturbs the equilibrium of the strong solvent(s) or other additives of the mobile phase, which is nonlinear. As a result of this perturbation, more peaks may be recorded than there are components in the injected sample. For example, the injection of a sample of the pure weak solvent may generate as many peaks as there are additives in the mobile phase, if these additives are all adsorbed by the stationary phase. These extra peaks have received a variety of names in the early literature. They have been called system peaks, pseudopeaks, ghost peaks, eigen peaks, vacancy peaks, induced peaks, etc. We call them system peaks. Note that not all system peaks are recorded this depends on the type of detector used. Also, system peaks may be positive or negative, depending on the experimental conditions. 

With reference to ions or ionic concentrations in ion exchange resin phase Perturbation component Reduced dimensionless variable... 

These experiments give information on the polarizability of excited molecules (from the amplitude of the oscillation), on the transverse phase relaxation times T2 (which depend on the cross sections of phase-perturbing collisions, Vol.l, Sect. 3.3), and on the population decay time T. For more details see [911, 913]. 

Table 3. Comparison of the effects of 3-aminobenzamide on Ho33342-induced cytotoxicity and cell-cycle phase perturbations in human adenocarcinoma cells and transformed fibroblasts...

Fig.3.11a-c. Phase perturbation of an oscillator by collisions (a) classical path approximation of colliding particles (b) frequency change of the oscillator A(t) during the collision (c) resulting phase shift... 

The elastic collisions do not change the amplitude, but the phase of the damped oscillator is changed due to the frequency shift As(jo R) during the collisions. They are often termed phase-perturbing collisions (Fig. 3.11). 

So far, we have neglected the fact that collisions also change the velocity of both collision partners. If the velocity component of a molecule is altered by an amount during the collision, the molecule is transferred from one subgroup (u Au ) within the Doppler profile to another subgroup vz+Uz EAv ). This causes a shift of its absorption or emission frequency from CO to co- -kuz (Fig. 3.21). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

In liquids, the distances / /(A, By) show random fluctuations analogous to the situation in a high-pressure gas. The linewidth Acoik is therefore determined by the probability distribution P(Rj) of the mutal distances i y (A, Bj) and the correlation between the phase perturbations at A caused by elastic collisions during the lifetime of the levels /, Ej (see the analogous discussion in Sect. 3.3). 

This causes a shift of its absorption or emission frequency from co to co kuz (Fig. 3.20). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

In this model of the phase-perturbed oscillator, both line broadening and line shift are proportional to the density N of collision partners and to the mean relative velocity v. The line broadening is determined by the cross section and the line shift by cjg (Fig.3.12). 

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