Phenomenological modifications

Non-Boussinesq convection. The Swift-Hohenberg model (17) is appropriate for the description of the so-called Boussinesq convection [42], when the dependence of thermophysical fluid parameters on temperature is disregarded. If this dependence is taken into account, a quadratic nonhnearity appears in the amplitude equations [43]. We shall use the following phenomenological modification of the SH equation for non-Boussinesq convection ... 

The co-ordination of theoretical and experimental results at higher e is realised either within the frameworks of phenomenological modifications of entropic theory... 

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

The traditional, essentially phenomenological modeling of boundary lubrication should retain its value. It seems clear, however, that newer results such as those discussed here will lead to spectacular modification of explanations at the molecular level. Note, incidentally, that the tenor of recent results was anticipated in much earlier work using the blow-off method for estimating the viscosity of thin films [68]. 

Smoluchowski theory [29, 30] and its modifications fonu the basis of most approaches used to interpret bimolecular rate constants obtained from chemical kinetics experiments in tenus of difhision effects [31]. The Smoluchowski model is based on Brownian motion theory underlying the phenomenological difhision equation in the absence of external forces. In the standard picture, one considers a dilute fluid solution of reactants A and B with [A] [B] and asks for the time evolution of [B] in the vicinity of A, i.e. of the density distribution p(r,t) = [B](rl)/[B] 2i ] r(t))l ] Q ([B] is assumed not to change appreciably during the reaction). The initial distribution and the outer and inner boundary conditions are chosen, respectively, as... 

Catalysis is a dynamic process, and deeper insights into its phenomenology are extractable from in situ measurements than from characterizations of catalysts before and after catalysis. A number of notable in situ experiments have relied on modifications of standard TEM operations under vacuum. The main functions of the EM depend on a high-vacuum environment, and the pressure in a TEM is usually of the order of 10-7-10-6 mbar. Because the influence of the reaction environment on the structure and activity of a catalyst is critical (3), the high-vacuum environment of a conventional EM is inappropriate for investigating a catalytic reaction, as are characterizations of catalysts in post-reaction environments (e.g., when the catalyst has been taken out of the reaction environment and cooled to room temperature). 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

More successful attempts to interpret yielding on a molecular level were based on an extension of the Eyring phenomenological flow theory by incorporating molecular characteristics [132,133]. The modification is based on changes in distribution of rotational conformation states of segments upon stress action and the effect of temperature on them. 

In the previous section, the phenomenological description of Brownian motion was presented. The Langevin analysis leads to a velocity autocorrelation function which decays exponentially with time. This is characteristic of a Markovian process, as Doobs has shown (see ref. 490). Since it is known heyond question that the velocity autocorrelation function is far from such an exponential function, the effect that the solvent structure has on the progress of a chemical reaction cannot be assessed very reliably by means of phenomenological Langevin description. Since the velocity of a solute is correlated with its velocity a while before, a description which fails to consider solute and solvent velocities can hardly be satisfactory. Necessarily, the analysis requires a modification of the Langevin or Fokker—Plank description. In this section, some comments are made on this new and exciting area of research. 

The main goal of simulation methods is to obtain information on the spatial and temporal behavior of a complex system (a material), that is, on its structure and evolution. Simulation methods are subdivided into atomistic and phenomenological methods. Atomistic methods directly consider the evolution of the system of interest at the atomic level with regard to the microscopic structure of the substance. These methods include classical and quantum MD and various modifications of the MC technique. Phenomenological methods are based on macroscopic equations in which the atomistic nature of the material is not directly taken into account. Within the multiscale approach, both groups of methods mutually complement each other, which permits the physicochemical system under study to be described most comprehensively. 

The phenomenological equation that determines the motion of the magnetic moment of a ferromagnetic sample is known generically as the Landau-Lifshitz-Gilbert equation and has two basic modifications. The first form... 

Moreover, this fitting shows that in the considered temperature-frequency landscape, only the temperature dependence of As = As(T) and r = x(T) is observed, while the other parameters B, (3, A, and q are not temperature-dependent. Thus, the proposed phenomenological model (114) as a modification of the CD function (21) with a conductivity term could be successfully applied for simultaneous fitting of dc-conductivity, the main process, and the EW presented in the master plots (see Fig. 27). 

Localized reactions at solid/liquid interfaces driven by focused laser light can be phenomenologically divided into deposition and dissolution processes as well as substrate modification. They can be used either for analytical or preparative purposes. An example is a direct writing procedure for the preparation of microstructures on macroscopic substrates without any masking technique. 

This novel effect has been termed non-Faradaic electrochemical modification of catalytic activity (NEMCA effect [5-15]) or electrochemical promotion [16] or in situ controlled promotion [20]. Its importance in catalysis and electrochemistry has been discussed by Haber [18], Pritchard [16] and Bockris [17], respectively. In addition to the group which first reported this new phenomenon [5-7], the groups of Lambert [12], Haller [10], Sobyanin [8], Comninellis [13], Pacchioni [21] and Stoukides [11] have also made important contributions in this area, which has been reviewed recently [14,15]. In this review the main phenomenological features of NEMCA for oxidation reactions are briefly surveyed and the origin of the effect is discussed in the light of recent kinetic, surface spectroscopic and quantum mechanical investigations. 

At this juncture we have in place a formalism that fully accounts for the refractive and dissipative modifications of the fundamental fields due to the dispersive electronic properties of the optical medium. This has been achieved not by any phenomenological or other ad hoc approach, but from first principles, using the theoretical methods of molecular QED. As a result, the necessary local field corrections in condensed media naturally emerge from the detailed form of the auxiliary field operators, obviating the need to encompass them indirectly in terms of macroscopic bulk susceptibilities, as is necessary in the semiclassical theory. 

The second type of resonance modification to energy denominators, alluded to earlier, is designed to reflect the finite lifetime of each molecular energy level, phenomenologically implemented by a modification of the corresponding energy... 

The relaxation forces are added to this equation as an afterthought to describe phenomenologically the behaviour of an isolated assembly of nuclear spins in an N.M.R. experiment. Further modification allows the description of chemical exchange. 

Ion Interaction. Ion-interaction theory has been the single most noteworthy modification to the computational scheme of chemical models over the past decade this option uses a virial coefficient expansion of the Debye-Huckel equation to compute activities of species in high ionic strength solutions. This phenomenological approach was initially presented by Pitzer ( ) followed by numerous papers with co-workers, and was developed primarily for laboratory systems it was first applied to natural systems by Harvie, Weare and co-workers (45-47). Several contributors to the symposium discussed the ion interaction approach, which is available in at least three of the more commonly used codes SOLMNEQ.88, PHRQPITZ, and EQ 3/6 (Figure 1). 

Essentially in the above modification, one interaction parameter x has been replaced with two new parameters j/ and 9, thus adding flexibility to the treatment. In doing so, a phenomenological approach of modeling has been adopted in place of the pseudolattice model we started with. 

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