Basic assumptions of the model

The semi-crystalline HDPE being modeled is initially of a sphernlitic morphology described in Chapter 2. It is made up of a 3D packing of crystalline lamellae and their attached amorphous layers as idealized in Fig. 9.25(a). The basic elements of the spherulite are two-phase composite inclusions that consist of integrally coupled crystalline lamellae and their associated amorphous layers between lamellae. Owing to their large aspect ratio, the composite inclusions are modeled as infinitely extended sandwiches with a planar crystalline/amorphous interface as shown in Fig. 9.25(b). Each composite inclusion I is characterized by its interface normal rt and the relative fractional thicknesses and / = 1 / of 

The model of large-strain plastic deformation and textnre evolution in HDPE is of a rigid plastic nature. It neglects elasticity and also pressure sensitivity of the 

The resistances to plastic flow of these slip systems that have been measured experimentally in highly textured QSC HDPE by Bartczak et al. (1992a) are given in Table 9.1. The chain slip system (100) [001] that has the lowest resistance is designated tq, which establishes it as an overall reference, and the other slip systems listed in the table have progressively higher plastic resistance. 

For operational ease in modeling, the kinetic shear-rate relation of Arrhenian form introduced in Section 9.4 is simplified for the simulations as a visco-plastic power law (Lee et al. 1993a), matched to the Arrhenian form at a given temperature, where the temperature dependence resides in part in a reference strain-rate factor 7o and in part in the exponent n.  

Because of chain inextensibility, the shear rate of any slip system is not dependent on the normal-stress component in the chain direction (Parks and Ahzi 1990). This renders the crystalline lamellae rigid in the chain direction. To cope with this problem operationally, and to prevent global locking-up of deformation, a special modification is introduced to truncate the stress tensor in the chain direction c. Thus, we denote by S° this modification of the deviatoric Cauchy stress tensor S in the crystalline lamella to have a zero normal component in the chain direction, i.e., by requiring that 5 c,c = 0, where c,- and c,- are components of the c vector (Lee et al. 1993a). The resolved shear stress in the slip system a can then be expressed as r = where R is the symmetrical traceless Schmid tensor of stress resolution associated with the slip system a. The components of the symmetrical part of the Schmid tensor / , can be defined as = Ksfw + fs ), where if and nj are the unit-vector components of the slip direction and the slip-plane normal of the given slip system a, respectively. 

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Consider a molecule consisting of more than three atoms, with an even number of valence elections, 2n (n > 2). The basic assumption of the model is that the... 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

Summing up, the selected Caco-2 data contain qualitative permeability measurements for 450 related (but chemically diverse) compounds that had been either collected from the literature or measured experimentally in laboratories connected with our group. Penetrating compounds were indicated by a score of +1, whereas a score of —1 was attributed to compounds having little (if any) ability to penetrate the epithelial cells. Passive permeation was used as a basic assumption of the model. 

If all the dimensionless parameters in a reaction model are kept constant with scale change, a similarity in the reactor performance is expected, provided that the basic assumptions of the model remain unchanged in both scales, e.g. in our example the plug flow condition of gas in the bubble phase. 

We have some misgivings about the basic assumptions of the model which leads to Equation (5.2-4). We fear that these assumptions oversimplify a very complex problem. 

Interpreting the small differences between the data and the predictions of the exponential tail requires caution, because some of the basic assumptions of the model are not soundly based. For example, it is assumed that the transport occurs at a well-defined mobility edge, with a temperature-independent mobility, and both points are open to question. Other effects, such as the internal electric fields of the contacts and deep trapping, lead to distortions of the current pulse from its ideal form. 

In an earlier publication (6) we considered the basic assumptions of the models. This chapter briefly reviews this subject and extends the tests by adding new results of the AH° of tetrabutylammonium bromide (Bu4NBr) in mixtures of water with acetonitrile (ACN) and with ethylene carbonate (EC) and preliminary results of some substituted and unsymmetrical tetraalkylammonium salts in mixtures of water with DMF. 

Recently, SX Wang et al. (1997, 2000e) have developed a model based on the direct-impact amorphization mechanism. This model can also be used to analyze the effects of variations in temperature, dose rate and ion mass. The basic assumptions of the model are ... 

The reason for the deviation of the C2v symmetry structures from the predictions of the simple model, while the D2h structures conform to it, lies in the basic assumptions of the model. The basic structure of the clusters was assumed to be circular, and deviations from this are treated as small perturbations of the system, resulting in the orbital energies shown in Fig. 9. The structure of the... 

A plot of In c/c ) vs t should therefore approach linearity with slope -Bj D/R an9 this is the region in which the basic assumption of the model (c/c 1.0) Is a valid approximation. 

The relativistic effective core potential method is reviewed. The basic assumptions of the model potential and pseudopotential variants are discussed and the reliability of both approaches in electronic structure calculations for heavy element systems is demonstrated for selected examples. 

The basic assumptions of the model have been introduced in Section 6.7. To adapt the model for aqueous solutions, we further assume that Ns solute molecules occupy the interstitial positions in the framework built up by the L-cules. Only one new molecular parameter is introduced in the new model, i.e., the interaction energy between the solute 5 and its surroundings, which we denote by Es-... 

A Maxwell type model of relaxation of stress is suggested by Radionov et al. (1986). The basic assumptions of the model include the velocity of relaxation of stress of non-homogeneity is proportional to the magnitude of stress, and inversely proportional to size L of non-homogeneity. As a result of analysis the next result is obtained the size of blocks of fractured rock mass is inversely proportional to strain rate, i.e. L = Ijs. Consider that when f 0, the value of L is limited, we may take... 

The various nonlinear rheological properties (e.g., viscosity ri and normal stress functions and N ) can then be correlated with P. This sort of argument and the basic assumptions of the model have been proven useful, as the model was previously found to fit steady-state data very well (3,4). 

Under the two basic assumptions of the model, we have found that the band edges are derived from the smallest eigenvalue Fmin of gap width is thus equal to ... 

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