Phenomenological representation

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Electron-Hole Recombination. A phenomenological representation of an electron-hole recombination process is shown in Figure 5. For illustration we assume that it is the electron that is the thermally-freed carrier although the discussion could just as well proceed on the basis that the hole is thermally liberated. 

Figure 5- Phenomenological representation of the thermal release of trapped electrons and their recombination with trapped holes to yield TL.

Equation (139) was already discussed elsewhere [22,23,31] as a phenomenological representation of the dynamic equation for the CC law. Thus, Eq. (139) shows that since the fractional differentiation and integration operators have a convolution form, it can be regarded as a consequence of the memory effect. A comprehensive discussion of the memory function (137) properties is presented in Refs. 22 and 23. Accordingly, Eq. (139) holds for some cooperative domain and describes the relaxation of an ensemble of microscopic units. Each unit has its own microscopic memory function m (t), which describes the interaction between this unit and the surroundings (interaction with the statistical reservoir). The main idea of such an interaction was introduced in Refs. 22 and 23 and suggests that mg(f) JT 8(f,- — t) (see Fig. 50). 

Fourier Transform Mechanical Analysis and Phenomenological Representation of Viscoelastic Material Behavior... 

The rate of viscoplastic flow is captured by a simple phenomenological representation ... 

FIGURE 3.31 Phenomenological representation for the velocities sign (left) and the electronic motion (right) in the energetic bands reduced at the first Brillouin zone after (Further Readings on Quantum Solid 1936-1967 Putz, 2006). 

In the cases where trapped entanglements are treated as real topological constraints Langley " has suggested a phenomenological representation for the modulus... 

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.

One can regard the Hamiltonian (B3.6.26) above as a phenomenological expansion in temis of the two invariants Aiand//of the surface. To establish the coimection to the effective interface Hamiltonian (b3.6.16) it is instnictive to consider the limit of an almost flat interface. Then, the local interface position u can be expressed as a single-valued fiinction of the two lateral parameters n(r ). In this Monge representation the interface Hamiltonian can be written as... 

The perturbation theory presented in Chapter 2 implies that orientational relaxation is slower than rotational relaxation and considers the angular displacement during a free rotation to be a small parameter. Considering J(t) as a random time-dependent perturbation, it describes the orientational relaxation as a molecular response to it. Frequent and small chaotic turns constitute the rotational diffusion which is shown to be an equivalent representation of the process. The turns may proceed via free paths or via sudden jumps from one orientation to another. The phenomenological picture of rotational diffusion is compatible with both... 

The Debye phenomenology is consistent with both gas-like and solidlike model representations of the reorientation mechanism. Reorientation may result either from free rotation paths or from jumps over libration barriers [86]. Primary importance is attached to the resulting angle of reorientation, which should be small in an elementary step. If it is... 

The phenomenological constants can be expressed in terms of experimental quantities. The Ly represents the interaction of component i with other particles of component/ In molten salts no component seems particularly suitable for serving as a solvent. The use of a volume fixed frame of reference for defining the fluxes gives a more symmetrical representation. The equations for the phenomenological constants are given by Sund-heim. ... 

The model proposed by Anderson and Phillips gives a phenomenological explanation of the properties of the amorphous materials without supplying a detailed microscopic description [42]. Low-temperature measurements of the specific heat of amorphous solids have however shown that instead of a linear contribution as expected from the TLS theory, the best representation of data is obtained with an overlinear term of the type [43,44] ... 

Purely phenomenological as well as physically based equations of state are used to represent real gases. The deviation from perfect gas behaviour is often small, and the perfect gas law is a natural choice for the first term in a serial expression of the properties of real gases. The most common representation is the virial equation of state ... 

A phenomenological model based on fundamental representations of the sensor structure and intrinsic processes has been proposed to explain the mechanism of signal formation [30, 31]. 

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