Effect phenomenological theory

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

In this section, we shall first give a brief review of the phenomenological theory of these effects.5 -6 26 We shall then show how the methods we have discussed in the previous sections may be extended to derive a microscopic theory of the relaxation effect the microscopic theory of electrophoresis will be considered in the next section. 

We want to analyze here the effect of these long-range Coulomb forces in the large friction limit (396) we shall thus consider the Brownian-dynamic approximation, which, as we shall see presently, gives exactly the same result as the classical semi-phenomenological theory developed in Section V-A. 

As has been described in 2.3, a polar crystal exhibiting spontaneous polarization Ps shows the intrinsic piezoelectricity due to strain-dependence of Ps (Sawada, 1961). The phenomenological theory of this effect will be described in the following. 

To thoughtful persons both in and out of the biological sciences, the existence and evolution of living organisms and their development have posed and continue to pose enormously challenging intellectual problems. Fritz London, who had contributed much to the phenomenological theory of superfluidity and superconductivity, was also fascinated by these problems. From his earlier work on superfluid helium and superconductivity he knew of the unifying effect that the existence of a Bose-Einstein condensate had upon a superfluid system. Today we would describe this as the effect on the system of the existence of an order parameter—in par-... 

The formulation of linear nonequilibrium thermodynamics is based on the combination of the first and second laws of thermodynamics with the balance equations including the entropy balance. These equations allow additional effects and processes to be taken into account. The linear nonequilibrium thermodynamics approach is widely recognized as a useful phenomenological theory that describes the coupled transport without the need for the examination of the detailed coupling mechanisms of complex processes. 

Researchers have examined the creep and creep recovery of textile fibers extensively (13-21). For example, Hunt and Darlington (16, 17) studied the effects of temperature, humidity, and previous thermal history on the creep properties of Nylon 6,6. They were able to explain the shift in creep curves with changes in temperature and humidity. Lead-erman (19) studied the time dependence of creep at different temperatures and humidities. Shifts in creep curves due to changes in temperature and humidity were explained with simple equations and convenient shift factors. Morton and Hearle (21) also examined the dependence of fiber creep on temperature and humidity. Meredith (20) studied many mechanical properties, including creep of several generic fiber types. Phenomenological theory of linear viscoelasticity of semicrystalline polymers has been tested with creep measurements performed on textile fibers (18). From these works one can readily appreciate that creep behavior is affected by many factors on both practical and theoretical levels. 

Nightingale, E.R., Jr. Phenomenological theory of ion solvation effective radii of hydrated ions. J. Phys. Chem. 1959, 63, 1381-1387. 

A simple quantitative model, with no adjustable parameters, is developed for the finite size effect of ferroelectric particles on the Curie transition temperature. As the size of ferroelectric particles decreases, the Curie temperature decreases. Based on our model for lattice contraction and the Landau-Ginsburg-Devonshire (LGD) phenomenological theory, size effects on Curie temperature of lead zirconate titanate PbZri. Ti Oj (PZT, x > 0.6) are considered. It is shown that Curie temperature of PZT (x > 0,6) decreases with decreasing particle size. The predictions of our equation are in agreement with the experimental results. 

M. Eikerling, Y.l. Kharkats, A.A. Komyshev, and Y.M. Volfkovich. Phenomenological theory of electro-osmotic effect and water management in polymer electrolyte proton-conducting membranes. Journal of the Electrochemical Society 145, 2684—2699 1998. 

In the frames of phenomenological theory we cannot discuss the resonant effects and will restrict ourselves with relaxation processes only. We will follow an approach proposed by Zener [7]. For a small-amplitude wave equation (6) represents Hooke s law in terms of stress, strain and stiffness... 

The Jahn-Teller effect requires quantum-mechanical description. Therefore, we will discuss the results obtained in a microscopic theory and later we will compare the expressions for ultrasonic absorption with one obtained in the phenomenological theory. 

In the preceding derivation of the frequencies of surface polaritons and surface excitons the boundary conditions were applied at a sharp boundary without surface currents and charges. In this simplest version of the theory the so-called transition subsurface layer has been ignored however, this layer is always present at the interface between two media, and its dielectric properties differ from the dielectric properties of the bulk. Transition layers may be of various origins, even created artificially, e.g. by means of particular treatment of surfaces or by deposition of thin films of thickness dphenomenological theory it is rather easy to take account of their effects on surface wave spectra in an approximation linear in k (15). 

J.E. Spanier and I.R Herman, Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous SiC films, Phys. Rev. B, 61, 10437-10450 (2000). 

Spanier, J. E. and Herman, I. P. (2000) Use of Hybrid Phenomenological and Statistical Effective-medium Theories of Dielectric Functions to Model the Infrared Reflectance of Porous SiC FIms. Phys. Rev. B, 61,10437-50. 

The first three terms on the right follow from Helfrich s free energy expansion in the curvature [13] as discussed in Sec. Ill of this chapter and are identical to the right-hand side of Eq. (4). The last term quantifies the finite size effect as mentioned at the end of Sec. V. A. It was introduced by Fisher [35] in his treatment of condensation and is widely used in phenomenological theories of nucleation (see, e.g.. Refs. 36 and 37). r has an estimated value on the order of 1. We note that the calculation of z from a model is far from trivial see, for example. Ref 38 for a discussion of the relatively simple case of on average flat interfaces. 

Nightingale ER (1959) Phenomenological theory of ion solvation. Effective raxhi of hydrated ions. 

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