Phenomenological descriptions, nature

This account of drug addiction might provide a phenomenological description of the behavior of the addict, but fails to identify its critical aspects. Thus, according to these accounts, the essential aspect of addiction is the automatic, habitual nature of responding. 

A phenomenological description of nature is necessarily incomplete. With every new step that is made in our understanding of the microscopic or molecular structure of matter there is an added compulsion to review our macroscopic knowledge and relate or reduce it in terms of molecular structure. The goal of this molecular approach is thus to understand the macroscopic properties of systems in terms of their molecular structures and ultimately to reduce the chemical constants to molecular constants. 

This section presents a phenomenological description of those aspects of solid-state NMR spectroscopy that are most useful for obtaining structural and dynamical information on phase transitions in minerals and the nature of disordered phases. The chemical shift and nuclear quadrupole interactions and their anisotropies receive particular emphasis, because they provide sensitive probes of the short-range structure, symmetry, and dynamics at the atomic position. Frequency shifts arising from these interactions can also serve as physical properties from which order parameters can be obtained for use in Landau-type treatments of the evolution toward a phase transition. 

Several different approaches have been utilized to develop molecular theories of chemical kinetics which can be used to interpret the phenomenological description of a reaction rate. A common element in all approaches is an explicit formulation of the potential energy of interaction between reacting molecules. Since exact quantum-mechanical calculations are not yet available for any system, this inevitably involves the postulation of specific models of molecules which only approximate the real situation. The ultimate test of the usefulness of such models is found in the number of independent macroscopic properties which can be correctly explained or predicted. Even so, it must be remembered that it is possible for incorrect models to predict reasonably correct macroscopic properties because of fortuitous cancellation of errors, insensitivity of the properties to the nature of the model, relatively large uncertainties in the magnitudes of the properties, or combinations of such effects. 

The other aspect consists in determining the properties and molecular nature of the objects responsible for the specific features of the functions C, R, and i. Within the framework of the theory of excitable media one may ignore the molecular mechanisms of activity and introduce some phenomenological description of the local properties of the medium. 

The phenomenological description of the excitability phenomenon given in Section 1.3 cannot claim to contain a final solution to the problem of the nature of transport systems of biological membranes responsible for nervous impuse generation. Where we stand, we can only conclude that the membrane as a whole is a nonlinear ion conductor whose properties are largely dependent upon the electrice field. For all that, the fact that the use of certain specific blocking compounds—tetrodotoxin and tetraethylammonium—allows the sodium and potassium ionic currents to be separated is alone sufficient to support the conception of selective transport systems located in the lipid matrix... 

The electrochemical interface is composed of molecules (solvent, adsorbed molecular species) and ions (ofelectrolyte), which can be partially discharged when chemisorbed, electrons and skeleton ions in the case of metal electrodes, electrons and holes in the case of semiconductor electrodes, mobile conducting and immobile skeleton ions in SEs. Molecules and ions are classical objects but electrons, holes with small effective mass, and protons are quantum objects. Interaction between molecules and surfaces is quantum-mechanical in nature in the case of chemisorption. Thus, microscopic description of the interface requires a combination of quantum and classical methods. One can benefit, however, from simple or more involved phenomenological descriptions of the interface. 

As follows from a brief review of the fundamentals on the kinetics of chain reactions, an elegant one-centered model of the process, which was offered at the begiiming of the development of the chain reaction theory, provides a phenomenological description. Initiation and inhibition of reactions by small additions of compormds, critical phenomena, etc. may serve as examples. However, it should be noted that modeling a chain reaction is usually complicated, if the one-centered approximation is not justified and in the cases when consumption of initial compormds should be taken into accormt, or when the intermediates are participating in the chain process, in other words if one has to deal with chain processes of a more complicated nature. So the efforts aimed at developing the special theoretical approaches that are thought to help for a better orientation in a complex chain chemical process are justified, in particular, rmder the conditions of multi-centered, and consequently multi-routed occurrance. 

The ability to trace a theory to its mathematical foundations can be used to distinguish an ab initio or first-principles theory from other types. In the context of alloy theory, for example, a theory remains first-principles as long as any approximations made as one proceeds from a formally exact expression of the Schrodinger equation are well understood in mathematical terms. Alternatively, the introduction of parameters (obtained through fits to experimental data or the consideration of certain limits in the mathematical expressions of the theory) in designing a model system break the smooth running of the mathematics. Theories so constructed may indeed provide a viable phenomenological description of natural phenomena but they cannot claim a priori justification of their content. 

Naturally, the clearest picture of the processes taking place during an elementary act is obtained by considering the mechanism on a molecular scale. However, any model used for a quantitative treatment of the problem as a rule introduces certain simplifications, thus making it difficult to obtain an exact interpretation of the experimental data. Hence, the molecular approach is successfully supplemented by the phenomenological description introduced by Frumkin in his well-known paper[8] establishing the connection... 

The fundamental challenge of physics has always been the understanding of the phenomenologically observed complexity in nature using a minimal set of simple principles. This reductionist program has historically-and for obvious reasons-concentrated mostly on studies of comparatively simple systems, deliberately avoiding more complex descriptions and phenomena. 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

Here, T is the appropriate state variable conjugate to the flux J and X, and depends on the thermodynamic state of the system. These linear, phenomenological laws are fundamental to all processes involving the transfer of mass, momentum or energy but, in many practical circumstances encountered in industry, the fundamental transport mechanisms arise in parallel with other means of transport such as advection or natural convection. In those circumstances, the overall transport process is far from simple and linear. However, the description of such complex processes is often rendered tractable by the use of transfer equations, which are expressed in the form of linear laws such as... 

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