Model phenomenological

Conservation equations together with constitutive equations describe a phenomenological model of the continuous medium (continuum). 

If one considers a liquid containing particles, then the disperse phase may be treated as a continuum, its description requiring a special phenomenological model with constitutive equations that differ from those relating to the continuous phase. 

The flux of mass and energy in a continuum occurs in the presence of spatial gradients of state parameters, such as temperature, pressure, or electrical potential. Variables such as the volume of a system, its mass, or the number of moles are called extensive variables because their values depend on the total quantity of substance in the system. On the other hand, variables such as temperature, pressure, mole fraction of components, or electrical potential constitute intensive variables because they have certain values at each point in the system. Therefore, constitutive equations express the connection between fluxes and gradients of the intensive parameters. In the constitutive equations listed above, the flux de- 

The weakness of this approach as first introduced by Narayanaswamy [3] is the assumption that a single relaxation time can describe the physical aging process accurately. Some improvement can be achieved by introducing the Kohlrausch-Williams-Watts (KWW) stretched exponential function [8] to describe the distribution of relaxation times eq ressed as  

In a similar way, Kovacs [9] has invoked a distribution of relaxation times to account for multiple relaxation events in the aging polymer, where each relaxation time depends on the glass structure and the temperature. The difference is that rather than trying to fit the observed heat capacity data, the movement of the enthalpy recovery peak in the DSC curves was followed, as discussed by Hutchinson [10]. This approach obviated the need to define a specific distribution of relaxation times. 

Several criticisms can be leveled at the phenomenological models the distribution of relaxation times is not easily defined, they give no information about the molecular relaxation processes involved and recently Simon and Bemazzani [16] found that 

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While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. 

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]. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Taking into account the hydration shell of the NA and the possibility of the water content changing we are forced to consider the water -I- nucleic acid as an open system. In the present study a phenomenological model taking into account the interdependence of hydration and the NA conformation transition processes is offered. In accordance with the algorithm described above we consider two types of the basic processes in the system and thus two time intervals the water adsorption and the conformational transitions of the NA, times of the conformational transitions being much more greater... 

If the above assumption is reasonable, then the modeling of most probable trajectories and of ensembles of trajectories is possible. We further discussed the calculations of the state conditional probability and the connection of the conditional probability to rate constants and phenomenological models. 

L. G. Austin, K. R. WeUer, and I. L. Kim, "Phenomenological Modelling of the High Pressure Grinding RoUs," XTTII International Mineral Processing Congress, Sydney, AustraUa, May 1993, pp. 87—95. 

Herbst et al. [International J. Mineral Proce.ssing, 22, 273-296 (1988)] describe the software modules in an optimum controller for a grinding circuit. The process model can be an empirical model as some authors have used. A phenomenological model can give more accurate predictions, and can be extrapolated, for example from pilot-to full-scale apphcation, if scale-up rules are known. Normally the model is a variant of the popiilation balance equations given in the previous section. 

PHENOMENOLOGICAL MODELING OF SERIES OF ANALYTICAL SIGNALS IN CASE OF COMPLEX CHARACTER OF THEIR FORM CHANGE... 

In previous researches it was shown that new phenomenological models are available to approximation any analytical peaks. These models can be used for modelling analytical experiments. 

The last class of models, which are widely used to describe amphiphilic systems, comprises the phenomenological models. As opposed to all the previous models, they totally ignore the fact that amphiphilic fluids are composed of particles, and describe them by a few mesoscopic quantities. In doing so, they offer the possibility of clarifying the interrelations between different behaviors on a very general level, and of studying universal characteristics which are independent of the molecular details. 

As already mentioned in the Introduction, phenomenological models for amphiphilic systems can be divided into two big classes Ginzburg-Landau models and random interface models. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

Richards, et. al. comment that while the exact relationship between the rule found by their genetic algorithm and the fundamental equations of motion for the solidification remains unknown, it may still be possible to connect certain features of the learned rule to phenomenological models. 

A phenomenological model for redox reactions in solution application to aquocobalt(III) systems. 

Quiben JM, Thome JR (2007b) Flow pattern based two-phase pressure drop model for horizontal tubes. Part II. New phenomenological model. Int. J. Heat and Fluid Flow. 28(5) 1060-1072 Rayleigh JWS (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Phil Mag 34 94-98... 

An essential requirement for device applications is that the orientation of the molecules at the cell boundaries be controllable. At present there are many techniques used to control liquid crystal alignment which involve either chemical or mechanical means. However the relative importance of these two is uncertain and the molecular origin of liquid crystal anchoring remains unclear. Phenomenological models invoke a surface anchoring energy which depends on the so-called surface director , fij. In the case where there exists cylindrical symmetry about a preferred direction, hp the potential is usually expressed in the form of Rapini and Popoular [48]... 

Mars, W.V. and Fatemi, A., A phenomenological model for the effect of R ratio on fatigue of strain crystallizing rubbers. Rubber Chem. Tech., 76, 1241, 2003. 

Commercial program packages that either propose phenomenological models or fit a given model to data are easily available such equations, along with the found coefficients can be entered into program TESTFIT. It is strictly forbidden to associate the found coefficients with physicochemical factors unless there is a theoretical basis for a particular model. 

In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious definition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159-163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the time constant. 

Enhancement of CHF subcooled water flow boiling was sought to improve the thermal hydraulic design of thermonuclear fusion reactor components. Experimental study was carried out by Celata et al. (1994b), who used two SS-304 test sections of inside diameters 0.6 and 0.8 cm (0.24 and 0.31 in.). Compared with smooth channels, an increase of the CHF up to 50% was reported. Weisman et al. (1994) suggested a phenomenological model for CHF in tubes containing twisted tapes. 

Nelson, R., and C. Unal, 1992, A Phenomenological Model of the Thermal Hydraulics of Convective Boiling during the Quenching of Hot Rod Bundles, Part I Thermal Hydraulic Model, Nuclear Eng. Design 756 277-298. (4)... 

Weisman, J., J. Y. Yang, and S. Usman, 1994, A Phenomenological Model for Boiling Heat Transfer and the CHF in Tubes Containing Twisted Tapes, Int. J. Heat Mass Transfer 37(l) 69-80. (4) Weisman, J., and S. H. Ying, 1983, Theoretically Based CHF Prediction at Low Qualities and Intermediate Flows, Trans. Am. Nuclear Soc. 45 832. (5)... 

The phenomenological equations proposed by Felix Bloch in 19462 have had a profound effect on the development of magnetic resonance, both ESR and NMR, on the ways in which the experiments are described (particularly in NMR), and on the analysis of line widths and saturation behavior. Here we will describe the phenomenological model, derive the Bloch equations and solve them for steady-state conditions. We will also show how the Bloch equations can be extended to treat inter- and intramolecular exchange phenomena and give examples of applications. 

Lorentzian line shapes are expected in magnetic resonance spectra whenever the Bloch phenomenological model is applicable, i.e., when the loss of magnetization phase coherence in the xy-plane is a first-order process. As we have seen, a chemical reaction meets this criterion, but so do several other line broadening mechanisms such as averaging of the g- and hyperfine matrix anisotropies through molecular tumbling (rotational diffusion) in solution. 

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