Time-dependent models

Noolandi and Hong (1978), Hong and Noolandi (1978a, 1978b). and Noolandi (1982) described solutions to the time-dependent Smoluchowski equation. In the long-time limit, Hong and Noolandi s results predict the recombination rate approaches a law as 

By Monte Carlo simulations, Ries et al. (1983, 1984) showed that the decay of the geminate recombination rate follows a t x relationship, where x 3/2. Both the time dependence and the initial recombination rate were dependent upon the thermalization distance. When the final recombination step was impeded by an energy barrier, the recombination kinetics could be described by an exponential time dependence. Results of the simulations show significant deviations from the asymptotic forms of the solutions of Hong and Noolandi. Within the time domain of experimental relevance, the simulated recombination rates were significantly larger. 

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Most modeling codes are a time-averaging technique. Depending upon the process, a time-dependent technique may be more suitable. Time-dependent modeling requires much more computing power than does time averaging. 

Markov analysis (Sec. 2.5.4) Evaluation of components systems, or functions Quantitative, time-dependent modeling process complc.s. success oriented has pcicniial for modeling complete nuclear plant... 

Techniques for quantifying Techniques used were basically from NUREG/CR-1278 or PRA Procedun s Guide, Chapter 4. (l)THERP (1980 version NUREG/CR-1278 with appropriate factors for a tree was used in procedure defined events. (2) A time dependent modeling approach was used to quantify operator actions during a sequence. THERPmethixlr. were ii ,cd as described in WASH- Id ... 

Before reviewing the results of pseudo-time-dependent models of homogeneous cloud interiors in detail, it is worthwhile to mention five successful predictions/ex-... 

Abstract. We present preliminary results of 3D hydrodynamical simulations of surface convection in red giants stars. We investigate the main differences between static ID and 3D time-dependent model stellar atmospheres of red giants for a range of metallicities between solar and [Fe/H] = —3 focusing in particular on the impact of 3D spectral line formation on the derivation of stellar abundances. 

Figure 27. Examples of diffusion of low-dose B implants (1 X 1014-2 X 1014 B atoms/cm2) during RTA for 10 s. Calculated curves are based on a time-dependent model described in the text.

The research interests of Rod Truax fall under the general heading of symmetry and supersymmetry and their applications to problems of chemical and physical interest. He is especially interested in finding the symmetry associated with time-dependent models and exploiting this symmetry to compute solutions to the quantum mechanical equations of motion. 

For a steady-state system, a time-dependent model is used because of the irregular shape of the atmospheric 14C02 record. This model accounts for radioactive decay of the 14C since 1950 explicitly, and it requires that we compare measured radiocarbon to a standard with a radiocarbon value that stays constant over time (Aabs). For ease, we define F here as ASN/Aabs [see Eq. (A1.4)] for samples measured since 1950 F equals A14C/1000 + 1. For a reservoir at steady state, the balance of radiocarbon entering and leaving the reservoir in year t is given by... 

Model calculations that include at least some of the reactions we have discussed for the syntheses of complex molecules have been performed in the last several years. Both steady-state and chemical time dependent models have been published. Unfortunately, as models include more and more complex species, they become more and more sensitive in their predictions to small changes. As an example, consider two models that in their predictions of the abundances of one-carbon-atom hydrocarbons differ by a factor of 3. This factor is not considered to be a major one in the field of interstellar chemistry. However, since the two-carbon-atom hydrocarbons are formed by reactions between one-carbon atom species, the model will differ in their predictions for the abundances of the larger hydrocarbons by a factor of 9. As one can easily discern, the situation becomes worse as the size of the hydrocarbons increase. Given this extreme sensitivity, modelers should attempt to make sure that at each stage of molecular complexity, they consider all depletion mechanisms and do not overestimate the abundances of the complex molecules that are intermediates in the formation of still more complex species. Unless this is done, models can become in our view overly optimistic about the growth of complexity in the interstellar medium. 

For both time-dependent and steady-state models, coherent dephasing is taken into account by phenomenological terms in the off diagonal time derivatives of the DM elements that appear in the Liouville dynamics. In the time dependent model, increasing the donor or bridge decoherences decreases the yield asymmetry and... 

The method used to represent the time dependent evolution of the solvent polarization that follows the transition between two different electronic states in the solute has been obtained as a generalization of the time-dependent model originally proposed to describe ground state charge-transfer phenomena within the PCM... 

Besides the sum-over-states and time-dependent models for the resonance Raman cross-section, other models can be used to calculate resonance Raman cross-sections, such as the transform and time correlator models. In the transform model, the resonance Raman cross-sections as a function of excitation energy, the excitation profiles, can be calculated from the absorption spectrum within the separable harmonic oscillator approximation directly by the following relationship [85-87]... 

Albarede F. (1998) Time-dependent models of U-Th-He and K-Ar evolution and the layering of mantle convection. Chem. Geol. 145, 413 -429. 

Gustafsson, B. G., 2000. Time-Dependent Modeling of the Baltic Entrance Area. 2. Water and Salt Exchange of the Baltic Sea. Estuaries, 23, 253-266. 

Time-Dependent Model (MultistageAVeibull, Time-to-Tumor Data) ... 

In comparing these results it is interesting to note that the values from the combined distributions are not greatly different between the full time-dependent model and the poly-3 corrected dichotomous model. This suggests that although clearly the full time-dependent model is preferable from a procedural point of view, the use of the poly-3 mortality correction is a reasonable substitute if needed, such as in cases where suitable software for the full multisite, time-dependent approach is unavailable. 

Vupputuri, R.K., The structure of the natural stratosphere and the impact of chlorofluoromethanes on the ozone layer investigated in a 2-D time dependent model. Pure Appl Geophys 117, 448, 1979. 

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