Phenomenological mechanisms

The first is the phenomenological mechanical theory. One form of the equation reads r6-9L... 

Viscoelastic stress analysis of two component systems shows that a broadening of the dispersion zone is to be expected 166,167), even if the disperse phase (filler) is purely elastic 166) and it is not necessary to ascribe different molecular properties to the continuous phase. The simplest way to visualize this mechanical interaction is by the use of phenomenological mechanically equivalent models. The model of Takayanagi (/68) is illustrated in Fig. 16. The elastic solution for this model is easily derived from elementary considerations. By the correspondence principle of viscoelastic stress analysis 169), the viscoelastic solution is obtained simply by substituting complex moduli in place of purely elastic moduli... 

Such being the case, further inferences about the nature of the wear process follow. A disrupted fluid film allows localized contacts at the rubbing surfaces, and it is the mechanistic processes at these contacts that determine the course of lubricated wear. When the wear process is abrasive, it is most likely influenced directly by fluid film thickness and surface roughness, whereas processes such as adhesion, transfer, oxidation, additive reaction and the like are responsive to surface conditions at the contacts as well as to the number of contacts. These are the aspects of lubricated wear that are emphasized in this chapter, from the viewpoint of phenomenology, mechanisms and modeling. 

Nearly all of the information available on the kinetics of heterogeneous reactions with lanthanide oxides concerns the C-type sesquioxides or the fluorite-related higher oxides. As stated in the section above, in these materials oxygen mobility is very high, whereas, metal-atom movement is extremely limited below 1200°C. Table 19 suggests the type of experiments that were done and the phenomenological mechanisms proposed before 1980 (Eyring 1979). 

In this chapter we describe the common forms of viscoelastic behaviour and discuss the phenomena in terms of the deformation characteristics of elastic solids and viscous fluids. The discussion is confined to linear viscoelasticity, for which the Boltzmann superposition principle enables the response to multistep loading processes to be determined from simpler creep and relaxation experiments. Phenomenological mechanical models are considered and used to derive retardation and relaxation spectra, which describe the time-scale of the response to an applied deformation. Finally we show that in alternating strain experiments the presence of the viscous component leads to a phase difference between stress and strain. 

Moran, N. (2007b). Rhythmic leaf movements physiological and molecular aspects. In Rhythms in Plants Phenomenology, Mechanisms, and Adaptive Significance (eds S. Mancuso S. Shabala), pp. 3-37. Springer-Verlag, Berlin. 

Besides the phenomenological mechanism mentioned above, there are many other physical mechanisms proposed to explain the positive ER facts. Those mechanisms will be discussed in more detailed manner in a future chapter. 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

These concluding chapters deal with various aspects of a very important type of situation, namely, that in which some adsorbate species is distributed between a solid phase and a gaseous one. From the phenomenological point of view, one observes, on mechanically separating the solid and gas phases, that there is a certain distribution of the adsorbate between them. This may be expressed, for example, as ria, the moles adsorbed per gram of solid versus the pressure P. The distribution, in general, is temperature dependent, so the complete empirical description would be in terms of an adsorption function ria = f(P, T). 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

For tliis model tire parameter set p consists of tire rate constants and tire constant pool chemical concentrations l A, 1 (Most chemical rate laws are constmcted phenomenologically and often have cubic or otlier nonlinearities and irreversible steps. Such rate laws are reductions of tire full underlying reaction mechanism.)... 

This difference is a measure of the free-energy driving force for the development reaction. If the development mechanism is treated as an electrode reaction such that the developing silver center functions as an electrode, then the electron-transfer step is first order in the concentration of D and first order in the surface area of the developing silver center (280) (Fig. 13). Phenomenologically, the rate of formation of metallic silver is given in equation 17,... 

In order to anticipate problems and to interpret observations under the extreme conditions of shock compression, it is necessary to consider structural and electronic characteristics of PVDF. Although the phenomenological piezoelectric properties of PVDF are similar to those of the piezoelectric crystals, the structure of the materials is far more complex due to its ferroelectric nature and a heterogeneous mixture of crystalline and amorphous phases which are strongly dependent on mechanical and electrical history. 

The simplified failure envelopes are not derived from physical theories of failure in which the actual physical processes that cause failure on a microscopic level are integrated to obtain a failure theory. We, instead, deal with phenomenological theories in which we ignore the actual failure mechanisms and concentrate on the gross macroscopic events of failure. Phenomenological theories are based on curve-fitting, so they are failure criteria and not theories of any kind (the term theory implies a formal derivation process). 

If it cannot be guaranteed that the adsorbate remains in local equilibrium during its time evolution, then a set of macroscopic variables is not sufficient and an approach based on nonequihbrium statistical mechanics involving time-dependent distribution functions must be invoked. The kinetic lattice gas model is an example of such a theory [56]. It is derived from a Markovian master equation, but is not totally microscopic in that it is based on a phenomenological Hamiltonian. We demonstrate this approach... 

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. 

With respect to the carrier mechanism, the phenomenology of the carrier transport of ions is discussed in terms of the criteria and kinetic scheme for the carrier mechanism the molecular structure of the Valinomycin-potassium ion complex is considered in terms of the polar core wherein the ion resides and comparison is made to the Enniatin B complexation of ions it is seen again that anion vs cation selectivity is the result of chemical structure and conformation lipid proximity and polar component of the polar core are discussed relative to monovalent vs multivalent cation selectivity and the dramatic monovalent cation selectivity of Valinomycin is demonstrated to be the result of the conformational energetics of forming polar cores of sizes suitable for different sized monovalent cations. 

In what follows, the phenomenology of carrier transport will be briefly reviewed along with the mechanism of the Valinomycin model of carrier transport. The development of the molecular structure of Valinomycin will be considered in some detail, since the key to the dramatic selectivity of Valinomycin is thought to reside in the energetics of the molecular structure. Confidence in an understanding of the molecular structure of the Valinomycin-cation complex becomes tantamount to confidence in the presented basis of ion selectivity. 

The interpretation of our CPG data is complicated by the presence of comparatively fast radiative and nonradiative decay channels for the singlet exciton, which compete with the field-induced dissociation. In order to provide a clear picture of the observed mechanism and disentangle it from the singlet exciton decay dynamics, we define the following phenomenological time-dependent parameter ... 

Thermodynamic, statistical This discipline tries to compute macroscopic properties of materials from more basic structures of matter. These properties are not necessarily static properties as in conventional mechanics. The problems in statistical thermodynamics fall into two categories. First it involves the study of the structure of phenomenological frameworks and the interrelations among observable macroscopic quantities. The secondary category involves the calculations of the actual values of phenomenology parameters such as viscosity or phase transition temperatures from more microscopic parameters. With this technique, understanding general relations requires only a model specified by fairly broad and abstract conditions. Realistically detailed models are not needed to un-... 

The polymerization of /3-(2-furyl) acrolein and some of its homologues by acids141 gave a similar phenomenology and thus, presumably, the mechanism is similar to that of the corresponding ketones. Their 7-radiation polymerization only proceeded in solution, probably because acidic substances were formed from the solvent142. ... 

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