Phase insensitive

The summation for the coefficient of the P2 term likewise includes phase insensitive contributions where I m = Im, but also now one has terms for which I = I 2, which introduce a partial dependence on relative phase shifts— specifically on the cosine of the relative phase shift. Again, this conclusion has long been recognized for example, by an explicit factor cos(ri j — ri i) in one term of the Cooper-Zare formula for the photoelectron (3 parameter in a central potential model [43]. 

If the output of the transducer is detected by a phase-insensitive circuit (as is usually the case), then it is the difference between the phases of the two rays that is important. This is... 

Rather phase-insensitive Norrish II photoproduct ratios are reported from irradiation of p-chloroacetophenones with a-cyclobutyl, a-cyclopentyl, a-cycloheptyl, a-cyclooctyl, and a-norbonyl groups [282], In each case, the E/C and cyclobutanol photoproduct ratios are nearly the same in neat crystals as measured in benzene or acetonitrile solutions. On this basis, we conclude that the reaction cavity plays a passive role in directing the shape changes of these hydroxy-1,4-biradicals. As long as the initial ketone conformation within the cavity permits -/-hydrogen abstraction (and these ketones may be able to explore many conformations even within their triplet excited state lifetime), the cavity free volume and flexibility allow intramolecular constraints to mandate product yields. 

Another example of phase-insensitive control utilizes the lambda scheme depicted in Fig. 7. In this case a strong coupling (o)2) field mixes an excited state with... 

Now, let us assume that the phase-sensitive device operates with a Gaussian signal with phase-insensitive noise. This is only an approximation to the real situation since realistic signals are discrete. Under such approximation the likelihood function corresponding to the detection of given data reads as... 

Here the variance a2 represents the phase-insensitive noise of each channel. The sampling of intensities may serve for an estimation of phase shift and the visibility simultaneously. Likelihood function (89) is maximized on the physically allowed space of parameters V < 1 by the following phase and visibility ... 

The study of optical lattices has been extended from ID to 2D and 3D using the phase-insensitive configurations mentioned above, and also by stabilization of the relative phases of the beams [30]. The spectra of such lattices has been studied by both absorption and emission techniques [24, 31, 32, 33, 34], as well as by photon correlation techniques [35, 36]. There have also been studies of lattices tuned far from resonance, using non-spectroscopic methods [37, 38]. ... 

The modulation structure of the resulting field ED(t) in front of the photodetector deserves a special discussion. In general, the Raman signal field from the sample cell consists of two components which can be characterized by a phase relationship between carrier and Raman sidebands corresponding to the cases of pure amplitude (AM) and frequency (FM) modulation (see Fig. 2). With the superposition of Eq and E by means of an analyzer, these AM and FM components lead to an amplitude and frequency modulation of the detector field Eo(t), respectively. The heterodyne beat signal of a phase-insensitive, square-lav photodetector now is connected only with the AM component of the Raman signal field and it can therefore be... 

The basic idea how to determine the directional dependence of the nonlinear polarization in a nonperturbative calculation is rather simple and is most easily demonstrated by an example. Let us first consider nonoverlapping laser fields within the RWA, and let us suppose that we only want to discriminate the (phase-insensitive) k2 emission from the (phase-sensitive) ki and 2k2 — ki contributions. Rewriting the overall polarization as... 

Wang, Z., Hagan, D. J., Van Stryland, E. W., and Assanto, G., Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities. Electron. Lett., 32, 1135-1136 (1996). 

While it is not essential to the method, frozen Gaussians have been used in all applications to date, that is, the width is kept fixed in the equation for the phase evolution. The widths of the Gaussian functions are then a further parameter to be chosen, although it appears that the method is relatively insensitive to the choice. One possibility is to use the width taken from the harmonic approximation to the ground-state potential surface [221]. 

The specific surface, a, is also relatively insensitive to the duid dynamics, especially in low viscosity broths. On the other hand, it is quite sensitive to the composition of the duid, especially to the presence of substances which inhibit coalescence. In the presence of coalescence inhibitors, the Sauter mean bubble size, is significantly smaller (24), and, especially in stirred bioreactors, bubbles very easily circulate with the broth. This leads to a large hold-up, ie, increased volume fraction of gas phase, 8. Sp, and a are all related... 

Whereas Hquid separation method selection is clearly biased toward simple distillation, no such dominant method exists for gas separation. Several methods can often compete favorably. Moreover, the appropriateness of a given method depends to a large extent on specific process requirements, such as the quantity and extent of the desired separation. The situation contrasts markedly with Hquid mixtures in which the appHcabiHty of the predominant distiHation-based separation methods is relatively insensitive to scale or purity requirements. The lack of convenient problem representation techniques is another complication. Many of the gas—vapor separation methods ate kinetically controUed and do not lend themselves to graphical-phase equiHbrium representations. In addition, many of these methods require the use of some type of mass separation agent and performance varies widely depending on the particular MSA chosen. 

Affinity values aie obtained by substituting concentiation foi activity in equation 4 foi the dye and, wheie appropriate, other ions in the system. A number of equations are used depending on the dye—fiber combination (6). An alternative term used is the substantivity ratio which is simply the partition between the concentration of dye in the fiber and dyebath phases. The values obtained are specific to a particular dye—fiber combination, are insensitive to hquor ratios, but sensitive to all other dyebath variables. If these limitations are understood, substantivity ratios are a useful measure of dyeing characteristics under specific appHcation conditions. 

Carriers and channels may be distinguished on the basis of their temperature dependence. Channels are comparatively insensitive to membrane phase transitions and show only a slight dependence of transport rate on temperature. Mobile carriers, on the other hand, function efficiently above a membrane phase transition, but only poorly below it. Consequently, mobile carrier systems often show dramatic increases in transport rate as the system is heated through its phase transition. Figure 10.39 displays the structures of several of these interesting molecules. As might be anticipated from the variety of structures represented here, these molecules associate with membranes and facilitate transport by different means. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

Detonation of 500-lb Lots of LE-3, An Insensitive Mono-Propellant , NOLTR-68-84 (1968) (Conf) J) Anon, Final Phase Report. Part I. 

In a discussion of these results, Bertrand et al. [596,1258] point out that S—T behaviour is not a specific feature of any restricted group of hydrates and is not determined by the nature of the residual phase, since it occurs in dehydrations which yield products that are amorphous or crystalline and anhydrous or lower hydrates. Reactions may be controlled by interface or diffusion processes. The magnitudes of S—T effects observed in different systems are not markedly different, which indicates that the controlling factor is relatively insensitive to the chemical properties of the reactant. From these observations, it is concluded that S—T behaviour is determined by heat and gas diffusion at the microdomain level, the highly localized departures from equilibrium are not, however, readily investigated experimentally. 

Another significant comparison between the two systems concerns the partial pressures of the metal dioxide molecules. These pressures are relatively insensitive to the condensed-phase composition and are quite similar in the plutonia and urania systems. Calculated metal dioxide vapor pressures are compared in Table V for 0/M = 1.96. 

Returning now to the subject of the chapter, in addition to appropriate retentive characteristics, a potential stationary phase must have other key physical characteristics before it can be considered suitable for use in LC. It is extremely important that the stationary phase is completely insoluble (or virtually so) in all solvents that are likely to be used as a mobile phase. Furthermore, it must be insensitive to changes in pH and be capable of assuming the range of interactive characteristics that are necessary for the retention of all types of solutes. In addition, the material must be available as solid particles a few microns in diameter, so that it can be packed into a column and at the same time be mechanically strong enough to sustain bed pressures of 6,000 p.s.i. or more. It is clear that the need for versatile interactive characteristics, virtually universal solvent insolubility together with other critical physical characteristics severely restricts the choice of materials suitable for LC stationary phases. 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

In the DEPT experiment, all the signals of the insensitive nuclei are in phase at the start of acquisition, so no refocusing period A (with accompanying loss in sensitivity) is required. Since the multiplets appear in-phase, it is called a distortionless experiment. Moreover, DEPT spectra depend on the angle 0 of the last polarization transfer pulse, and are less dependent on the delay times between the pulses. An error of 20% in the estimation of/values still affords acceptable DEPT... 

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