Continual approach

This represents a special case of high-level turbulence at a surface by the formation of steam and the possibility of the concentration of ions as water evaporates into the steam bubbles . For those metals and alloys in a particular environment that allow diffusion-controlled corrosion processes, rates will be very high except in the case where dissolved gases such as oxygen are the main cathodic reactant. Under these circumstances gases will be expelled into the steam and are not available for reaction. However, under conditions of sub-cooled forced circulation, when cool solution is continually approaching the hot metal surface, the dissolved oxygen... 

Surface force apparatus has been applied successfully over the past years for measuring normal surface forces as a function of surface gap or film thickness. The results reveal, for example, that the normal forces acting on confined liquid composed of linear-chain molecules exhibit a periodic oscillation between the attractive and repulsive interactions as one surface continuously approaches to another, which is schematically shown in Fig. 19. The period of the oscillation corresponds precisely to the thickness of a molecular chain, and the oscillation amplitude increases exponentially as the film thickness decreases. This oscillatory solvation force originates from the formation of the layering structure in thin liquid films and the change of the ordered structure with the film thickness. The result provides a convincing example that the SFA can be an effective experimental tool to detect fundamental interactions between the surfaces when the gap decreases to nanometre scale. 

In the Euler-Euler models, i.e., the TFMs, it is assumed that both the gas and the solid phase are interpenetrating continua. This continuous approach is especially useful and computationally cost-effective when the volume fractions of the phases are comparable, or when the interaction within and between the phases plays a significant role in determining the hydrodynamics of the system. As discussed before, it is relatively straightforward to model the gas phase, for instance by the use of well-established CFD techniques. The challenge is to establish an accurate hydrodynamic description of the particulate phase. 

Ions of opposite charge will continually approach, and to offset this tendency, a repulsive energy term, which is only important at short range, must be added. 

The principal implication of the continuous approach is the assumption of continuity across a trait that is indexed on a continuum. The primary implication of a categorical approach—whether it is monothetic, polythetic,... 

A curve that continually approaches a given line but does not meet it at any... 

In the design of an automated analytical instrument, or selection of the most appropriate commercially available type, the choice between the discrete and continuous approach is fundamental. Both types are considered in detail under the various technique... 

Comprehensive 2D HPLC can be also operated under stop-flow mode. In this case, after transferring a desired fraction volume onto the secondary column, the flow of the mobile phase in the first dimension is stopped and the fraction analyzed in the second dimension. When the separation is finished, the mobile-phase flow in the first dimension is switched on and the whole procedure is repeated again for the analysis of all the transferred fractions. The disadvantage of this procedure is the long analysis time, while the advantage can be that the second-dimension column can give higher plate numbers if compared to the continuous approach [23]. 

Yebra-Biurrun and S. Cancela-Perez, Continuous approach for ultrasound-assisted acid extraction-minicolumn preconcentration of... 

Two procedures are commonly used for rapid radiochemical separations, the batch approach and the continuous approach. In the batch approach, the desired activities are produced in a short irradiation, separated and counted with the procedure being repeated many times to reduce the statistical uncertainty in the data. In the continuous approach, the production of the active species is carried out continuously, and the species is isolated and counted as produced. 

The present modeling approach to circadian cancer chronotherapy is based on an automaton model for the cell cycle. Continuous approaches to cell cycle progression have also been used to study the link between cell proliferation and circadian rhythms [44] and to determine, in conjunction with optimal control theory, the most efficient circadian schedules of anticancer drug administration [45]. Including more molecular details of the cell cycle in continuous models for cell populations represents a promising line for future research. Hybrid models incorporating molecular details into the automaton approach presented here will also likely be developed. 

Keywords Carbon nanotubes Hubbard model Continual approach Non-linear equations Regular solutions Soliton lattices... 

We shall consider single walled carbon nanotube (SWNT) with low limit of radius (Fig. 1). This implies that the transition to continual approach is imposable along SWNT perimeter. On the figure the Z axis is directed along nanotube axis and I axis - along SWNT perimeter. We study so-called zig-zag or (n, 0) SWNT, where n - a number of hexagons on the tube perimeter. In order to apply Fourier analysis it is assumed the (n, 0) tube is infinite in Z axis direction. 

The behavior of Equation (34) near h->0 is due to the assumption, involved in its derivation, that the free energy can be approximated by the internal energy. Such an assumption is likely to be valid only for sufficiently thick films, since the entropy is negligible in such cases. In contrast, particularly for submonoiayer coverages, the entropy rather than the interactions between the atoms of the film plays the major role In addition, for film thicknesses smaller than about 5 layers, the continuous approach should be replaced by a discrete one. 

The continuous approach is more recent and is not yet widely used. In contrast to a discontinuous procedure, the adsorptive is now continuously feeding the adsorbent, so that the point on the adsorption isotherm is continuously moving along the path of the isotherm. By using the term adsorption isotherm we imply that the adsorption system is always at thermodynamic equilibrium. Since the system is now continuously changing we should stricdy speak of quasi-equilibrium (Rouquerol et at., 1988). The fact that this condition was not fulfilled in the first experiments of this type (Innes, 1951 Lange, 1963) unfortunately delayed the development of this procedure. 

The birth and death functions now have the same units as the population balance. To attempt a solution, an integral or continuous approach will be used in place of this discrete summation. This suggests that there is a continuous distribution of particle sizes (i.e., the sizes of interest for the population balance are much larger than that of singlets, doublets, etc.). Some key substitutions for this integration are necessary ... 

DISCRETE VERSUS CONTINUOUS APPROACHES TO ULTRASOUND-ASSISTED SAMPLE PREPARATION... 

Most applications of USASD are discrete In nature. This can be ascribed to the fact that few research groups have so far worked on continuous approaches despite such major advantages as automation and reduced chemical consumption. Because automation Is one of the main goals In developing continuous systems, the best way of performing batch digestion steps In an automated manner Is by using a robot to mimick the operations carried out manually by an operator [14],... 

Continuous approaches outperform DUSAL in some respects. In the last two decades, automation has been one growing trend in technology and also in analytical chemistry [9]. The most salient advantages of automated analytical methods based on CUSAL over those relying on DUSAL are as follows ... 

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