Non-stationary process

That is, without some measure of control, the process is unstable and will diverge from the set point. Unlike a stationary process, which will achieve a steady state at some point, a non-stationary process requires some sort of integral control. 

A procedure similar to the condensate separation in the imperfect Bose gas was employed by Lifshitz and Pitaevski [78]. The diagrammatic technique allows us to calculate the reaction rate and steady-state joint correlation functions. A separation of a condensate from terms with k = 0 cannot be done without particle production (p = 0), in which case nA, tiq —> 0 as t —> oo. In this respect the formalism presented by Lushnikov [111] for the non-stationary processes is of certain interest. 

For non-stationary processes the motion of the center of mass produced by external sources (sound waves for instance) can be coupled to the electro-nuclear system via its total momentum operator p (cf. eq.(9)). Not only vibrational excitations but also electronic ones can be mediated by non-stationary motion of the center of mass. This is a feature related to the stationary frame determined by a particular stationary electronic state. 

First, it is of common interest to unsteady processes and their models. Chemical unsteadiness must be taken into account in many cases. For example, studies with variations in catalyst activity, calculations of fluidized catalyst bed processes (when the catalyst grain "is shaking in a flow of the reaction mixture and has no time to attain its steady state), analyses of relaxational non-stationary processes and problems of control. Unsteady state technology is currently under development [14,15], i.e. the technology involving programmed variation of the process parameters (temperature, flow rate, concentration). The development of this technology is impossible without distinct interpretation of the unsteady reaction behaviour. 

V.L. Tataurov and V.I. Ivanov, Non-stationary Processes in Catalysis, Institute of Catalysis, Novosibirsk, 1979, Part 2, pp. 170-175 (in Russian). 

In practice, the construction of function fi is connected with considerable limitations in the sphere of knowledge to which the subject of investigation refers. In the sphere of remote monitoring these limitations are explained by the presence of unsolved problems when optimizing the choice of the most informative wavelengths as well as by the absence of efficient methods to study non-stationary processes. Therefore, in the field of remote monitoring, both expert and empirical knowledge is combined at the level needed to study partial models for transition to a comparative analysis by criterion fi. 

An analysis of the recent observation data [30,31] shows that baroclinic Rossby waves that are generated off the eastern coasts in the northern parts of the Pacific and Atlantic oceans in a period of about a year represent their dominant non-stationary dynamical response to the annual cycle of the atmospheric forcing in the latitudinal range from 10-15° to 45-50°N. In so doing, their mean phase velocities (0.02-0.03 ms 1 at 40-45°N) are higher than the theoretical values (about 0.01 ms-1). A similar situation is observed in the Black Sea as well [27]. In [32], several reasons of this phenomenon were listed such as the interaction with more large-scale non-stationary processes, topographic and nonlinear effects, and insufficient duration and spatiotemporal resolution of the observation data. 

Characteristic time Fo defines dimensionless duration of non-stationary process and in inverse proportion to a square of characteristic thickness of bed8ch and in direct ratio an effective temperature conductivity a. For example, for increase of capacity of heat process in HHP it is necessary to reduce time of process. Active reduction of physical time of process will be promoted by reduction of thickness of bed8Ch and increase in its temperature conductivity a. 

Duration and intensity of non-stationary processes heat and mass transfer in hydride beds is determined by dimensionless criteria Fourier number - Fo and Biot number - Bi. Their relationship with physical parameters is given by formulas ... 

Criterion Biot determines the ratio of intensity of external heat exchange processes (numerator) and effective thermal conductivity of a hydride layer (denominator). To carry out frontal chemical reactions of hydrogen sorption -desorption, small numbers Biot (Bi<0.1) are preferable. Number Bi can be decreased by several ways 1) decreasing of the characteristic layer size 2) decreasing of intensity of an external heat transfer (but time of non-stationary processes is growing) 3) increasing of effective hydride bed thermal conductivity. 

Non-stationary operations have found large scale industrial application. An important classical example is catalytic cracking, where oil is exposed with a short residence time to a rapidly deactivating zeolitic catalyst, which is regenerated in a second step by removal of deposited coke. A novel non-stationary process is selective butane oxidation over a regenerable oxidation catalyst (see Chapter 2). Undoubtedly we will see more examples of this type of process, in which the proper catalytic step and the regeneration of the catalytic sites occur in different compartments under different conditions. A nice application involves... 

A theoretical analysis has been carried out for galvanostatic and potentiostatic pulse regimes [27]. The idea that developed is a bit the same as backflushing with pressure driven-membrane operation such as microfiltration or ultrafiltration. The time dependencies of the extent of the concentration polarization near the membrane surface during the pulse are described theoretically for both pulse regimes and a qualitative discussion of the pause duration is presented. The main characteristic of the non-stationary process is the transition time between the state without polarization and the state with stationary polarization. 

When evaluating the results of ternary copolymerizations by means of the Alfrey-Gold-finger scheme, the stationary character of copropagation should be critically established. With non-stationary processes, the uncertainty of interpretation becomes more serious, even when the experimental results agree with theory. 

Given a realization s(t) of a non-stationary process, one can estimate its spectrum (i.e. calculate the wavelet sample spectrum) using a wavelet g t) by... 

Polarimetric effects predicted by this model have not been foimd up to now. We note, however, that the accretion of CS matter onto yoimg stars is essentially the non-stationary process. Therefore the hot-spot parameters can be highly variable. Besides, in the young stars surrounded by a CS disks there is a stronger mechanism of light polarization that can mask the thin effect discussed above (see below). 

Such idealised conception of two reactionary zones (liquid monomer phase and interphase layer on the boundary liquid monomer-solid polymer ) allowed ns to obtain the quantitative kinetic model of stationary and non-stationary processes for three-dimensional polymerisation and to explain their special peculiarities [23-25]. 

The two main classes of random processes are the stationary and non-stationary processes. A stationary process (or strict(ly) stationary process) is a stochastic process whose probability distribution at a fixed time or position is the same for all times or positions. As a result, the basic feature of stationary processes is that their statistical properties (mean, standard deviation and so on) do not change over time. 

Conversely, an example of a non-stationary process is given by the stochastic models of fatigue crack propagation in general the resulting crack propagation process becomes a non-stationary random process of time, whose mean and standard deviation increase with time. The objective of the correspondent models is to describe how the crack size pdf, or at least its statistics, vary in time or, alternatively, to describe the statistics of the time to reach a given crack size. 

The non-stationary process related to the natural circulation prompts the attention for the time-variant aspect of the reliability analysis of thermal-hydraulic passive systems. 

Shapoval VI, Reznik GV (1974) On the theory of non-stationary processes of electroreductirai of anions in molten salts (chronopotentiometry). In Ionic melts, vol 2. Naukova Dumka, Kiev, pp 135-149... 

So, the proposed kinetic models of non-stationary processes in the form of equations (4.42) and (4.45) are based on hypotheses on the microheterogeneity of the polymerization system and on the special role of the interface layer on the feolid polymer-liquid oligomer boundary. All characteristics of the bulk polymerization up to the high conversion state are explained, including the S-like character of the stationary kinetics curves, the number-average molecular weight of a polymer via the post-polymerization process and the presence in it of at least two characteristic sections determined by the life times of active primary and secondary radicals in the interface layer. 

Thus, the rate of radical s concentration changing under non-stationary process conditions can be described by the expression... 

In our case, non-stationary processes are analyzed, i.e. the values of factors depend on time t. Classical apphcation of Bayesian method is not correct in this case, because observations obtained in different time moments represent the other state of the indicators. The modified application of Bayesian method for the calculation estimates of parameters of non-stationary process mathematical models is presented in research papers (Augutis et al, 2012 Zutautaite-Seputiene et al, 2010). 

Here it should be emphasized that, in contrast to the effects of chemical media influence, physical media effects are reversible. However, component parts can also fail due to physical media effects, because incorporated media molecules may cause swelling of the plastics. Because media absorption is a non-stationary process, the outer area swells first, while the interior of the material remains unaffected. Internal stresses arise in the material which, beyond a certain strain level, can lead to cracking and thus ultimately to failure. However, desorption, not absorption, is the more critical factor here. Desorption may cause tensile stresses in the outer zones that result in cracking (see Section 1.4.3). Unless the micro structure of the material is damaged, swelling is a reversible physical media effect [93]. 

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