Model cylinder

The cylinder model is used to characterize the helices in the secondary structure of proteins (see the helices in Figure 2-124c),... 

Where helical secondaiy structures are represented by the cylinder model, the /i-strand. structures are visualized by the ribbon model (see the ribbons in Figure 2-124c). The broader side of these ribbons is oriented parallel to the peptide bond. Other representations replace the flat ribbons with flat arrows to visualize the sequence of the primary structure. 

A variation on the exact soiutions is the so-caiied seif-consistent modei that is explained in simpiest engineering terms by Whitney and Riiey [3-12]. Their modei has a singie hollow fiber embedded in a concentric cylinder of matrix material as in Figure 3-26. That is, only one inclusion is considered. The volume fraction of the inclusion in the composite cylinder is the same as that of the entire body of fibers in the composite material. Such an assumption is not entirely valid because the matrix material might tend to coat the fibers imperfectiy and hence ieave voids. Note that there is no association of this model with any particular array of fibers. Also recognize the similarity between this model and the concentric-cylinder model of Hashin and Rosen [3-8]. Other more complex self-consistent models include those by Hill [3-13] and Hermans [3-14] which are discussed by Chamis and Sendeckyj [3-5]. Whitney extended his model to transversely isotropic fibers [3-15] and to twisted fibers [3-16]. 

Figure 3-26 Self-Consistent Composite Cylinder Model...

Among the several known types of carbon fibres the discussion in this chapter is limited to the electric arc grown multi-walled carbon nanotubes (MWCNTs) as well as single-walled ones (SWCNTs). For MWCNT we restrict the discussion to the idealised coaxial cylinder model. For other models and other shapes we refer to the literature [1-6],... 

An image of an MWCNT obtained by using all available reflexions usually exhibits only prominently the oo.l lattice fringes (Fig. 4) with a 0.34 nm spacing, representing the "walls" where they are parallel to the electron beam. The two walls almost invariably exhibit the same number of fringes which is consistent with the coaxial cylinder model. 

The diesel engine is one of the most widely used global powcrplants and can be found in almost every conceivable application. From small single-cylinder models to V20 designs, their horsepower can range from as low as 3.73 kW (5 hp) to as high as 46,625 kW... 

The point source model assumes that the fire can be represented as a point that is radiating to a target at a distance, R, from the point. The model is most appropriate for calculating incident heat fluxes to targets where fluxes are in the range from 0 to 5 kW/m (SFPE, 1999). The point source model has been shown to be accurate for calculating the incident heat flux from a jet flame to a target outside the flame (Beyler, 2002). The literature contains more refined line or cylinder models (Beyler, 2002 SINTEF, 1997). 

Zhou, L.M. and Mai. Y.W. (1992). A three-cylinder model for evaluation of sliding resistance in fiber pusb-out test, in Ceramics Adding the Value (M.J. Bannister, ed.), CSIRO Pub, Melbourne, pp. 1113-1118. 

Fig. 7.9. Schematic illustrations of the interphase in (a) three eyiindcr model and (b) four cylinder model.

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

Before proceeding to a review of both scaled particle theory and fuzzy cylinder model theory, it would be useful to mention briefly the unperturbed wormlike (sphero)cylinder model which is the basis of these theories. Usually the intramolecular excluded volume effect can be ignored in stiff-chain polymers even in good solvents, because the distant segments of such polymers have little chance of collision. Therefore, in the subsequent reference to wormlike chains, we always mean that they are unperturbed . 

With increasing polymer concentration, we may expect that the polymer global motion changes from the fuzzy cylinder model mechanism to the repta-tion model mechanism. The onset of the crossover should depend on the degree in which the lateral motion of a polymer chain is suppressed by entanglement with its surrounding chains, but it is difficult to estimate this degree. There are some disputes over it in the case of flexible polymers [20]. 

Values of B calculated from the ordinate intercepts are shown in Fig. 23 as a plot of B/(2q)3 against the number of the Kuhn segments N. For N<4, the data points for the indicated systems almost fall on the solid curve which is calculated by Eq. (78) along with Eqs. (43), (51), (52), and Cr = 0. A few points around N 1 slightly deviate downward from the curve. Marked deviations of data points from the dotted lines for the thin rod limit, obtained from Eq. (78) with Le = L and de = 0, are due to chain flexibility the effect is appreciable even at N as small as 0.5. The good lit of the solid curve to the data points (at N 4) proves that the effect of chain flexibility on r 0 has been properly taken into account by the fuzzy cylinder model. 

In this article, we have surveyed typical properties of isotropic and liquid crystal solutions of liquid-crystalline stiff-chain polymers. It had already been shown that dilute solution properties of these polymers can be successfully described by the wormlike chain (or wormlike cylinder) model. We have here concerned ourselves with the properties of their concentrated solutions, with the main interest in the applicability of two molecular theories to them. They are the scaled particle theory for static properties and the fuzzy cylinder model theory for dynamical properties, both formulated on the wormlike cylinder model. In most cases, the calculated results were shown to describe representative experimental data successfully in terms of the parameters equal or close to those derived from dilute solution data. 

Hard-sphere or cylinder models (Avena et al., 1999 Benedetti et al., 1996 Carballeira et al., 1999 De Wit et al., 1993), permeable Donnan gel phases (Ephraim et al., 1986 Marinsky and Ephraim, 1986), and branched (Klein Wolterink et al., 1999) or linear (Gosh and Schnitzer, 1980) polyelectrolyte models were proposed for NOM. Here the various models must be differentiated in detail—that is, impermeable hard spheres, semipermeable spherical colloids (Marinsky and Ephraim, 1986 Kinniburgh et al., 1996), or fully permeable electrolytes. The latest new model applied to NOM (Duval et al., 2005) incorporates an electrokinetic component that allows a soft particle to include a hard (impermeable) core and a permeable diffuse polyelectrolyte layer. This model is the most appropriate for humic substances. 

Blissett et al. (1997) used the concentric cylinder model of Powell et al. (1993) to obtain residual stresses, whereas Boccaccini (1998) utilised the results of a simple force balance in 1-D performed by Wang et al. (1996), which gives the residual thermal stresses in the matrix along the axial direction as ... 

Extraneural Cull-electrodes are available in two variations. The early split cylinder models consist of SILASTIC designs which have a stiff closing mechanism and only a few electrode channels. They have to be carefully adjusted to the nerve diameter. 

Wormlike chain model Wormlike touched beads model Wormlike cylinder model... 

Fig. 37a-c. Schematic representation of various wormlike chain models 67) d is the diameter of the touched bead and cylinder models... 

The 1-D concentric cylinder models described above have been extended to fiber-reinforced ceramics by Kervadec and Chermant,28,29 Adami,30 and Wu and Holmes 31 these analyses are similar in basic concept to the previous modeling efforts for metal matrix composites, but they incorporate the time-dependent nature of both fiber and matrix creep and, in some cases, interface creep. Further extension of the 1-D model to multiaxial stress states was made by Meyer et a/.,32-34 Wang et al.,35 and Wang and Chou.36 In the work by Meyer et al., 1-D fiber-composites under off-axis loading (with the loading direction at an angle to fiber axis) were analyzed with the... 

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