Pseudo-time-dependent models

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

Smaller molecules tend in general to show less of a temporal effect with abundwces at early time being closer to steady-state abundances. Another key result of pseudo-time-dependent models is that large abundances of neu atomic carbon are present at early time. Pseudo-time-dependent models represent an improvement over steady-state models because the chemist can be investigated at eras before steady state is reached. Early time abundances are particularly interesting because it is important to realize that large abundances of complex molecules can be produced fairly quickly. 

How sensitive are calculated abundances to dissociative recombination branching ratios In order to answer this question, Millar et al. (1987) have attempted to use the Bates approach to estimate branching ratios for a wide variety of polyatomic ions, to incorporate the results into a pseudo-time-dependent model of dense clouds, and to... 

All of these types of chemical models - steady-state, pseudo-time-dependent, and fully time-dependent - are themselves dependent on rate coefficients which are often highly uncertain and which need to be determined b experimental and/or theoretical techniques before the models can be put on a sound basis. Tlie approach in this review will be to... 

Herbst (1988) adopts "pseudo time-dependence in which the chemistry is followed in time within a static cloud in which density and temperature are fixed. Van Dishoeck (1988) has argued that chemistry in diffuse clouds is achieved so rapidly that the time dependence need not be followed. In each approach, the modeller chooses a set of reactions describing the chemistry of the species of interest, and uses an appropriate mathematicsd model to obtain either time dependent or steady state results to compare with observations. The comparison should then yield astrophysical information. The lack of uniqueness in such information has been... 

Hassel GE, Herbst E, Bergin EA (2010) Beyond the pseudo-time-dependent approach chemical models of dense core precursors. Astron Astrophys 515 A66. doi 10.1051/0004-6361/200913896... 

Data evaluation Model parameters were obtained by fitting of experimental time dependencies of pressure in the lower cell compartment to theory. Obtaining of theoretical time - pressure courses represents integration of mass balance (partial differential equation, or, assuming pseudo-steady-state, ordinary differential equation). 

We, however, suggest that the time gap between generation and expulsion from the deep Are Formation relative to the shallower Spekk Formation, and time dependent HC loss from traps, i.e. the pseudo-steady-state model of loss and replenishment discussed in this paper and in Paper I, is the reason why we today generally do not observe type Ill/coal derived gas in the traps off Mid-Norway. Thus, the time lag between, even delayed expulsion from the Are Formation, and expulsion from the shallower Spekk Formation is simply too significant in light of the dynamic trap model (cf. Sales 1993, 1997—trap type II and III), for these traps to hold on to petroleum generated e.g. 50Mabp. 

The results show in the preceding graph that the steady-state solutions (dashed) map well onto the transient solutions for the concentrations of B and D at early time. Beyond 8000 time units, the steady-state concentrations begin to deviate noticeably from the full solutions. This is also the time at which the concentration of A begins to rise above near-zero values. The steady-state solutions are useful because they allow us to compute the flow rate of reagent A and the time dependence of the systems with very simple equations, but we cannot push such an analysis too far beyond its region of applicability. From the perspective of analysis, the pseudo-steady state is important to us because it explains the behavior of the more complex and complete model in a very straightforward way. 

Fixed bed decoking involves time-dependent profiles of the oxygen concentration and the carbon load both within the particles (pore diffusion) and within the fixed bed (moving reaction zone). The reaction zone migrates through the reactor, which may lead to overheating of the catalyst, if the velocity of the zone is too fast. To model the coke burn-off process in the adiabatic fixed bed the so-called one-dimensional pseudo-homogeneous reactor model can be used. 

The range of time-dependent, finite strain constitutive models for rubbery materials is quite limited. Perhaps the most simple and effective models are the so called pseudo stress and pseudo strain models introduced by Schapery [49]. 

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