Revival fractional

Linear a-olefins were produced by wax cracking from about 1962 to about 1985, and were first commercially produced from ethylene in 1965. More recent developments have been the recovery of pentene and hexene from gasoline fractions (1994) and a revival of an older technology, the production of higher carbon-number olefins from fatty alcohols. 

Under even more intense photoexcitation ( 10mJ/cm2), the coherent A g and Eg phonons of Bi and Sb exhibit a collapse-revival in their amplitudes (Fig. 2.10) [42,43], This phenomenon has a clear threshold in the pump density, which is common for the two phonon modes but depends on temperature and the crystal (Bi or Sb). At first glance, the amplitude collapse-revival appears to be analogous to the fractional revival in nuclear wavepackets in molecules [44,45]. However, the pump power dependence may be an indication of a polarization, not quantum, beating between different spatial components of the coherent response within the laser spot [46],... 

Migration of fluids in a porous matrix with solid-liquid fractionation results in a process much similar to the chromatographic separation of elements (DeVault, 1943 Korzhinskii, 1970, Hofmann, 1972). This mechanism has recently been revived in the context of mantle metasomatism by Navon and Stolper (1987), Bodinier et al. (1990), Vasseur et al. (1991), in the context of hydrothermal systems by Lichtner (1985) and, for stable isotopes, by Baumgartner and Rumble (1988). Only a simplified account of this model will be given here. Let

solid matrix and melt, respectively, and vHq the fluid velocity relative... 

The double-spike technique of Rosman (1972) has been revived by Tanimizu et al. (2002), who used a Zn- Zn spike and obtained precisions in the range of a fraction of a per mil. Jackson and Gunther (2003) describe a laser-ablation technique of isotopic measurement, which provides a precision comparable to the standard solution nebulization methods. 

The first step in the dynamics, the S Sj deactivation, is completed in only 52 1 fs, presenting the expected monoexponential decay profile, as can be seen in Figure 8-1 la. This figure shows the fraction of trajectories in each state between 0 and 200 fs for the 35 trajectories computed. Between 20 and 30 fs and again at 37 fs it is possible to observe a revival of the S2 state occupation. The fraction of trajectories in Sj is not shown in the figure for sake of clarity. It is just complementary to the fraction of trajectories in S2. Thus, a revival in S2 is companied by a decrease in Sj occupation. The revivals in the S2 occupation occur when the total number of... 

More recently, the use of the chloroformate-aqueous alkali method has been revived by G. R. Barker and his associates in order to prepare a suitably protected D-ribose carbonate for a synthesis of a-D-ribofuranosyl phosphate. (An analogous synthesis of the latter compoimd, involving a phosgene-pyridine reaction, appeared almost simultaneously. ) Condensation of D-ribose with methyl chloroformate in the presence of aqueous sodium hydroxide led to the formation of a mixture of the anomers of l,5-di-0-(methoxycarbonyl)-D-ribofuranose 2,3-carbonate (LII), which was resolved by fractional recrystallization. The treatment of either of the derived D-ribofuranosyl chlorides with methanol and silver carbonate... 

The proliferation of powerful and diversified procedures for protein fractionation, generally based on relatively small differences in the physicochemical properties of the proteins in the mixture, has almost totally outdated the older procedures, particularly organic solvent fractionation based on the accentuation or induction of such differences. The reasons for such neglect are well known and have been emphasized by S. Kaufman (1971), who tried several years ago to revive organic solvent fractionation, which is frequently no more laborious or incomplete and of no lower yield than many other techniques claimed to be particularly suitable. 

The AIChE Bubble Tray Design Manual (AIChE, 1958 Gerster et al., 1958) presented the first comprehensive estimation procedure for numbers of transfer units. For many years this remained the only such procedure available in the open literature the work of organizations like Fractionation Research Incorporated (FRI) was available only to member companies. However, during the last 15 years or so there has been a revival of distillation research and other comprehensive estimation procedures have been published (e.g., Zuiderweg, 1982 Chan and Fair, 1984a). We summarize these methods below. The text by Lockett (1986) provides an excellent summary of what is available in the open literature on distillation tray design for those interested in further study. 

In 1946, Will and Lenze s method was revived once again by Ashford, Cooke, and Hibbert in Canada. Starch nitrates were fractionated in acetone and alcohol, and were examined for their nitrogen content and their molecular weight (lowest for the alcohol-soluble fractions). A nitrate from the B-fraction (branched) was reported to be less stable than one from the A-fraction, a not unlikely possibility. 

However, the classic Lewis idea that fibrillation results from the activity of a small number of rapidly firing reentrant circuits that give rise to wavefront fractionation and fibrillatory conduction has been revived. Experimental models have identified localized rotors due... 

J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, Periodic spontaneous collapse and revival in a simple quantum model, Phys. Rev. Lett. 44 (1980) 1323. l.Sh. Averbukh, N.F. Perel man, Fractional revivals Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics, Phys. Lett. A 139 (1989) 449. 

Recently, there has been a renewed interest in the de Broglie-Bohm formulation of quantum mechanics as a numerical tool to perform multidimensional wave packet calculations [13-15]. It has also been used to visualize the motion of quantum mechanical wave packets by trajectories and to study the transition from quantum mechanics to classical mechanics [16-18]. Carlsen and Goscinski [16], for instance, have studied fractional and full revivals of circular Rydberg wave packets in the hydrogen atoms using this formulation. 

An independent line of thought also revives our interest in energy densities. The standard global hybrid functionals [2] mix a large constant fraction of a semilocal (LDA, GGA, or meta-GGA) exchange energy with a complementary... 

Averbukh, l.S. and Perelman, N.F., Fractional revivals Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics, Phys. Lett., 139,449,1989. 

In this section, the real-time spectra for two different pump probe cycles, i.e. two-color and one-color real-time experiments, are presented. First, the two essentially different real-time spectra I t) are analyzed in the time domain, followed by a detailed analysis in the frequency domain (/(u )). Introducing the spectrogram technique I At,uj)) enables detailed insight into the investigated wave packet dynamics. In particular, it visualizes directly several total and fractional revivals of induced vibrational wave packets. By comparing the spectrograms of the different pump probe cycles, one can easily assign the different ionization pathways of the laser-induced processes. This nicely demonstrates the different excitation mechanisms in the two experiments. 

This discussion makes clear that the spectrogram technique enables us to characterize the varied wave packet dynamics for the two different pumpfeprobe cycles. The discussion nicely demonstrates the value of spectrograms for the analysis of wave packet phenomena as total and fractional revivals. Moreover, the spectrograms allow the identification of ionization pathways in pump probe experiments. Hence, spectrograms are excellent tools for an improved analysis of wave packet propagation phenomena, compared to real-time and Fourier spectra only. 

Fractional Revivals of Vibrational Wave Packets in the NaK State... 

Owing to anharmonicities of the PES, a wave packet normally spreads. As a first consequence the amplitude of the oscillation decreases with increasing time after preparation, i.e. a destruction of the wave packet appears. However, this spreading is not at all an irreversible one. In their detailed description of the long-term evolution of wave packets Averbukh and PerePman [54, 355] discussed the phenomena of wave packet revivals and fractional revivals. At a wave packet revival the wave function of the prepared system can be subject to a certain sequence of reconstructions which provide regular, well-localized structures in the probability density. The form of each condensation of the probability density is directly determined by the shape of the initial wave packet. The revival time Tpev is given by... 

Here, long-time dynamics of an initially extremely cold ensemble of NaK molecules excited to its electronic A state are presented. This will allow a detailed observation of revival structures. As a rough estimate, the occurrence of the total revival can be calculated from spectroscopic data [357] to be at Trev 190 ps- The low temperature of the molecular beam, combined with its high stability and the extremely low pulse-to-pulse fluctuations of the laser system used, enabled for the first time the real-time detection of fractional revival structures in a molecular system. 

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