Phase nonstationary

Selectivity of chromatographic separation is known to be varied by changing both the nonstationary phase composition and adsorbent nature. It is shown that the less are the values of the reached selectivity coefficient the higher are the requirements to column effectiveness. In this connection the choice of stationai y phase with high and predicted selectivity coefficient for the compounds being separated is still remains a topical problem of high-performance liquid chromatography. 

Experience profound compositional shifts in use May experience phases changes in use Site in the disease s location Operate at variable drug activity Highly nonstationary state kinetics Application technique and amount are highly individualized Applications short-acting Local tissue levels tied to efficacy Used on diseased, damaged skin No easy bioequivalency endpoint Systemic absorption absolutely undesirable, but some unavoidable... 

One of the interesting consequences of eqs. (11-25) and (11-26) is the dependence of the probability of the molecule being in a given nonstationary state on the time correlations in the coupled radiation field. In most experimental studies the radiation field employed consists of a superposition of many frequencies with random phases. It is convenient to represent that form of field in terms of a correlation function d>(t, t"), which is defined in eq. (6-16). Introducing, because of the polychromaticity of the radiation field, the averages of eqs. (11-25) and (11-26), choosing the same representation for the field correlation function as did Bixon and Jortner, and using the conservation of probability, we find for the probability of dissociation of the molecule the relation ... 

For the description of nonstationary processes in a periodic reactor, the CBR is used. The equations for gas-phase and surface component concentrations are described by the ODE system. 

Figure 1. The creation, evolution, and detection of wave packets. The pump laser pulse pump (black) creates a coherent superposition of molecular eigenstates at t — 0 from the ground state I k,). The set of excited-state eigenstates N) in the superposition (wave packet) have different energy-phase factors, leading to nonstationary behavior (wave packet evolution). At time t = At the wave packet is projected by a probe pulse i probe (gray) onto a set of final states I kf) that act as a template for the dynamics. The time-dependent probability of being in a given final state f) is modulated by the interferences between all degenerate coherent two-photon transition amplitudes leading to that final state.

Such systems are realized first of all in pilot plants for pyrolytic preparation of active carbon, for instance, by means of the fluidization of an oxidizing agent into the solid phase in a nonstationary regime. The related heat-transfer equation contains the convection term and that of the heat effects of the chemical reaction ... 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

G I Golodets, Possible causes of nonstationary phenomena in gas phase radical chain oxidation in the presence of transition metal oxides, Kinet Catal (Engl) 28 1074 (1987)... 

A mathematical model to be solved numerically has been developed and used to predict the separation effects caused by nonstationary conditions for a liquid membrane transport. Numerical calculations were made to compute pertraction characteristics such as input and output membrane selectivity (ratio of respective fluxes), concentration profiles for cations bound by a carrier in a liquid membrane phase, and the overall separation factors. These quantities are discussed as dependent... 

The area of the hysteresis loop increases as Tr 1 [19]. The power a is the same as that of the 1 /fa noise. This is the case of nonstationary Hamiltonian chaos in the mixed phase space [20]. The power of the 1 // is greater than 1, a > 1. We will return this point in Section IV. 

The effect of random noise on nonstationary motions has been recently studied to examine the stability of the long-time tails in Hamiltonian dynamics [15], where the survival time distribution for a particle trapped in a potential well is studied under random perturbations. The results were very clear the Weibull distribution describes the intermediate long-time regime in the same manner shown in the case of cluster formation, but the contribution of the log-Weibull distribution completely disappears in the intrinsic long-time regime and the Gumbel distribution takes the phase of it. The details will be reported in a... 

Yablonovitch [215] proposed using a medium with a rapidly decreasing in time refractive index ( plasma window ) to simulate the so-called Unruh effect [216] the creation of quanta in an accelerated frame of reference. More rigorous and detailed studies of quantum phenomena in nonstationary (deformed) media have been performed [159,160,217-229]. The case when the dielectric constant changes simultaneously with the distance between mirrors (in one dimension) was also considered [230,231]. Johnston and Sarkar compared the spectra of photons created by the motion of mirrors and by the time variations of the dielectric permeability [232]. An analog of the nonstationary Casimir effect in the superfluid 3He, namely, the friction force on the moving interface between two different phases, was discussed by Volovik [233]. 

Thus, the first trials provided rather confusing results on the primary processes of rhodopsin photoisomerization. The first group then reported several femtosecond pump probe studies, one after another, which involved the measurement of bovine rhodopsin with a wide spectral window [47] and the measurements of 9-cis rhodopsin [48] and 13-demethyl rhodopsin [49]. In addition, they observed oscillatory features with a period of 550 fs (60 cm-1) on the kinetics at probe wavelengths within the photoproduct absorption band of rhodopsin, whose phase and amplitude demonstrate that they are the result of nonstationary vibrational motion in... 

The electric field envelope of the femtosecond pump pulse which is short compared to the period of the oscillations in Fig. 15.3 (b) covers a frequency range much broader than the energy spacing of individual levels of the low-frequency mode. In other words, the pump spectrum overlaps with several lines of the vibrational progression depicted in Fig. 15.1 (b). As a result, impulsive dipole excitation from the Vqd = 0 to 1 state creates a nonstationary superposition of the wavefunc-tions of low-frequency levels in the Vqd = 1 tate with a well-defined mutual phase. This quantum-coherent wavepacket oscillates in the Vqd = 1 state with the frequency Q of the low-frequency mode and leads to a modulation of O-H stretching absorption which is measured by the probe pulses. In addition to the wavepacket in the Vqd = 1 state, impulsive Raman excitation within the spectral envelope of... 

In the case of nonstationary mass transfer in a steady-state translational Stokes flow past a spherical drop with limiting resistance of the continuous phase, the steady-state value Shst is presented in the first row of Table 4.7. By substituting this value into (4.12.3), we obtain... 

Because the initial vibrational state for absorption spectra often is v = 0, the vibrational nonstationary state typically produced initially is an only slightly distorted Gaussian wavepacket centered at R"g. Conservation of momentum requires that this approximately minimum-uncertainty wavepacket be launched at the turning point on the upper surface, R e = R"g, which lies vertically above R"g. [This is a consequence of the stationary phase condition, see Sections 5.1.1 and 7.6 and Tellinghuisen s (1984) discussion of the classical Franck-Condon... 

This short time apparent decay is a particularly interesting intramolecular dephasing process, which merely accounts for the fact that the individual molecular eigenstates in the summation in (2.21) all have slightly different energies, . When the molecule is initially prepared in the nonstationary state or with some other set of a ,, there is a coherent superposition of all of these molecular eigenstates with relative phases which are fixed. However, because of the differences between the energies, , these phases become different at a subsequent time, the exp[ —... 

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