Stationary model

We begin with a stationary model of addiction, in which the temptation to hit can depend on the addiction level but otherwise remains constant over time, which allows us to identify some basic insights. We first ask what is the direct implication of self-control problems by comparing TCs and naifs. In the stationary model, naifs are always more likely to hit than TCs. Since naifs are unaware of future self-control problems, they perceive that they will behave exactly like TCs in the future and... 

Of course, since the incentive effect is driven by future restraint, it can be operative only if there is some future period where people would refrain in the face of pure pessimism. Consider the implications of this point in a stationary model. If in period 1 people would hit when "unhooked" in the face of pure pessimism, then in all periods they would hit when unhooked in the face of pure pessimism, and therefore the incentive effect cannot be operative. In contrast, if in period 1 people would refrain when unhooked in the face of pure pessimism, then in all periods they would do so, and therefore the incentive effect can be operative. This logic implies that if people are initially unhooked, the incentive effect can be operative if and only if people would refrain without it. Since the pessimism effect makes sophisticates more likely to hit than nails, we can therefore conclude that sophisticates are more likely than naifs to become addicted starting from being unhooked. 

In this section, we analyze a stationary model of addiction ... 

Example 1 illustrates some basic intuitions of the stationary model. We now show that these intuitions hold more generally. To do so, we focus on the case where there is an infinite horizon (T= ). We do so for two reasons. First, it is expositionally easier to describe the results for an infinite horizon. Second, this assumption is closer in spirit to the rational choice models of addiction and yields more realistic results. 

Part 1 of proposition 1 merely restates lemma 1 Naifs are always more likely to hit than TCs. Part 2 of proposition 1 establishes that the surprising outcome of example 1—that sophisticates consume more of the addictive product than naifs—always holds in a stationary model when people are initially unhooked. 

These results stand in stark contrast to the results in the stationary model. In the stationary model, the incentive effect is operative if and only if in the first period people would refrain when unhooked in the face of pure pessimism, and as a result sophisticates can suffer a very harmful lifelong addiction because of a feeling that addiction is inevitable. In the youth model, in contrast, as long as the temptation to consume eventually falls to the point at which people would choose to refrain even in the face of pure pessimism, the inevitability of addiction vanishes, and as a result sophisticates are less likely to hit than naifs and unlikely to suffer harmful lifelong addictions. 

Finally, we note that although we have no formal results concerning the behavior of naifs, there is reason to believe that naifs are likely to do quite poorly in the youth environment. Recall that in the stationary model... 

Quasi-stationary models assume that, besides their spatial distribution, the temperature of the fast electrons also does not evolve during the ion acceleration process. These issues do not seem to provide a major problem when determining the maximum ion energy, since the acceleration of these ions (which will be the most energetic) takes place over a time scale over which the temperature and the entire distribution do not vary appreciably [93]. 

Linear stationary systems with regular fluxes are realized mostly in laboratory conditions, whereas technology deals with systems in nonsteady-state and/or random fluxes. Nevertheless, the linear stationary model is enough simple and sometimes effective for semi-empirical treatment of various experimental data (first of all adsorption-desorption) even obtained on materials obviously prepared in conditions of random fluxes. 

Initially these facilities were supposed to be constructed for the front-line troops thus, they were to be mobile (on wheels) and capable of delousing the gear of 400 men per hour. As developments progressed, the stationary model was given preference. These were to be set up at troop reassignment centers. The facilities were to be accessible within a few hours or at most a day. 

Another problem in the quantal approach is that ions in solution are not stationary as pictured in the quantum mechanical calculations. Depending on the time scale considered, they can be seen as darting about or shuffling around. At any rate, they move and therefore the reorientation time of the water when an ion approaches is of vital concern and affects what is a solvation number (waters moving with the ion) and what is a coordination number (Fig. 2.23). However, the Clementi calculations concerned stationary models and cannot have much to do with dynamic solvation numbers. 

Note that, in the quasi-stationary model, equation (8.148) does not contain the term with the second derivative d /dt. ... 

The molecular configuration is a function of time. Molecular systems are not stationary molecules vibrate, rotate, and tumble. Force field calculations and the properties predicted by them are based on a. stationary model. What is needed is some way to predict what motions the atoms within a molecule will undergo at various temperatures. Molecular dynam-ics (MD) simulations use classical mechanics—force field methods—to study the atomic and molecular motions to predict macroscopic properties. "... 

A body-fixed frame can easily be defined without the introduction of constraints among the dynamical coordinates of the problem. Observe that the system is invariant to the 0(3), the orthogonal rotation group. And, as aoi rotates so does the stationary model electronic state function. The electron-nucleus separation problem is hence solved in a manner differing radically from the standard approach. 

Special attention has been given to the treatment of the permanent MqSo term in the harmonic development of the tidal potential. It is obvious that the choice of the quasi-stationary model — either the "zero" or the "mean" state — is decisive. The "zero" case is to be preferred from the point of view of Physical Geodesy while the "mean" case shows some advantages for hydrographical or oceanographic applications. The difference between the tidal reduction values for precise levellings corresponding to the "zero"... 

The effect of sonic irradiation on drying of particulate materials in a fluidized bed was analyzed by Kardashev and coworkers (1972). Considering a quasi-stationary model of a fluidized bed in which the voids are assumed to be cylinders of radius r and length L, the following equations were developed for drying rate in a classical fluid bed of particulate material ... 

Static instabilities induce a shift of the equilibrium point to a new steady-state point Ledinegg instability, boiling crisis, bumping, geysering, or chugging are all static instabilities since they can be analyzed using only stationary models. 

The thermal vibrations produce a more diffused distribution of the electron density than does a stationary model, increasing the atomic effective volume, making the interference within the atom more noticeable, and making consequently the decrease in the atomic scattering factor more rapid (see Figure 4B). 

Stationary models (Recknagle et ah, 2003 lora et ah, 2005 Ji et ah, 2006 Zhu et ah, 2005 Haberman and Young, 2005), however, do not answer the fundamental questions are steady-state solutions stable What is the fate of small temperature disturbances in the stack The response of the SOFC stack to the step change in total current at constant feed utilization has only been studied numerically in one work (Achenbach, 1995) (see the discussion below). 

As when analysing a time series, the stationarity of the disturbance signal is an important characteristic to consider. If the output is not stationary, then all the data must be differenced in order to obtain a stationary model. If the data is differenced k times, then the disturbance model will be of the form... 

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