Circular fibers

Figure 3-32 Halpin-Tsai Calculations (Circles) versus Adams and Doner s Calculations for E2 of Circular Fibers in a Square Array (After Halplrt ar d Tsai [3-17])...

Figure 3-38 Modified Halpin-Tsai Calculations versus Adams and Conner s Calculations for G 2 Circular Fibers In a Square Array (After Hewitt and de Malherbe [3-23])...

L. B. Greszczuk, Microbuckling Failure of Circular Fiber-Reinforced Composites, AIAA Journal, October 1975, pp. 1311-1318. 

Tex is the fiber linear density expressed in g/km. N/tex, which is numerically equivalent to GPa/SG, is a unit widely used in the textile industry and very useful to characterize non-circular fibers. 

When solutions of directly acting choUnomimetics are applied to the eye (i.e., conjunctival sac), they cause contraction of the smooth muscle in two important structures, the iris sphincter and the ciliary muscles (Fig. 12.3). Contraction of the iris sphincter decreases the diameter of the pupil (miosis). Contraction of the circular fibers of the ciliary muscle, which encircles the lens, reduces the tension on the suspensory ligaments that normally stretch and flatten the lens, allowing the highly elastic lens to spontaneously round up and focus for near vision (accommodation to near vision). 

Ascend M-G. A first estimation of prestress in co-called circularly fibered osteonic lamellae. J Biomech. 1999 32 935-942. 

Covering power The ability of fibers to occupy space. Noncircular fibers have a greater covering power than circular fibers. 

The cross-sectional shape of a fiber can affect many properties, e.g. luster, density, optical properties, feel of the fabric and an important characteristic called the covering power of a fabric. Covering power is the ability of fibers to occupy space. The reader can easily visualize that fibers having a circular cross-section will have a lesser covering power than fibers having a lobed cross-section. Noncircular fibers can provide a greater density in a fabric than circular fibers. 

An imaging spectrograph differs from a conventional (e.g., Czerny-Turner) design in that it maintains the one-to-one correspondence of the entrance slit and its image at the detector. So a circular fiber positioned at the entrance... 

Edie DD, Fain CC, Melt spun non-circular fibers from mesophase pitch. Carbon 86, Proceedings of the International Conference on Carbon, Baden-Baden, FRG, 629-631, 1986. 

The tunica albuginea consists of two layers, the outer of which is oriented longitudinally and the inner layer consisting of circular fibers. The inner layer contains struts that course the cavernosal space and... 

Fam, A. Z. and Rizkalla, S. H. (2001a), Confinement model for axially loaded concrete confined by circular fiber-reinforced polymer tubes , ACI Structural Journal, Vol. 98, Issue 4, pp. 451-461. 

Figure 18.5 Biomimetic scaffold for tympanic membrane replacement based on poly(ethylene oxide terephthalate)-co-poly(butylene terephthalate) and fabricated using additive manufacturing to deposit radial and circular fibers onto an electrospun basement mesh. Zoomed-in micrograph shows human mesenchymal stromal cells stained with methylene blue.

Cross-section. The cross-section of a fiber can be observed using a microscope. It has been found that the cross-sectional shape of a fiber can have a significant effect on its thermal insulation characteristics (Varshney et al., 2011). A fiber s cross-section with more trapped air may provide higher thermal insulation than a perfectly cylindrical fiber. For example, a hollow fiber traps more air inside its structure than a solid circular fiber. This is the reason why hoUow-fiber based fabrics can provide higher thermal insulation than solid circular-fiber based fabrics. In the same fashion, a noncircular fiber, say with a trilobal or scalloped oval surface, can trap more air than a circular fiber, because of its shape. Relatively large amounts of air trapped by noncircular fibers ultimately enhance thermal insulation characteristics (Matsudaira et al., 1993 Murakami etal, 1978). 

A detailed numerical study (Bond 2005) has shown that for the same overall fiber volume fraction, the diffusion coefficient D is rather insensitive to the spacing or distribution of circular fibers, although, in the case of composite laminates, the presence of a resin-rich interlaminar region would affect the overall value of the transverse component of D. 

Small circular fibers are better encapsulated within human tissue than larger fibers with... 

Fibers of noncircular cross section can modify and change both functional and aesthetic properties in textile structures. The triangular cross section is typical in those respects its shape leads to a stifler fiber than circular fiber of the same cross-sectional area, and in a fabric this results in less drapability and a crisper surface feel. Also, the flat surfaces reflect light in a different way than do curved surfaces and can create desirable lustrous... 

Most of the chapter is devoted to the construction of ray paths and their classification on circular fibers with axisymmetric profiles. However, we also consider noncircular fibers since cross-sections can differ from circular symmetry in practice, e.g. elliptical fibers. Finally, since this chapter parallels Chapter 1 to a large extent, it may be helpful to compare the results of corresponding sections. 

Fig. 2-1 Nomenclature for describing circular fibers. Cartesian coordinates X, y, z and cylindrical polar coordinates r, , z are oriented so that the z-axis lies along the fiber axis. A representative graded profile varies over the core and is uniform over the cladding, assumed unbounded.

Fig. 2-7 Schematic distribution of rays on circular fibers according to the value of the invariants andTfor (a) the step-profile of Eq. (2-8) and (b) the clad power-law fibers of Eq. (2-43) [3]. Shading denotes tunneling rays (TR) and hatching denotes refracting rays (RR). Bound rays (BR) occupy the unshaded regions.

We assume a circular fiber with refractive-index profile n(r,z). The local velocity of light is c/n(r, z) and the transit time over length z of the fiber is therefore given by... 

Since I is an invariant for the circular fiber we deduce that p(z) r- z) is also invariant, whence... 

In Chapters 1 and 2 we identified refracting rays within the cores of planar waveguides and circular fibers. The important feature of such rays is the bifurcation of the path at each reflection from the core-cladding interface. Here we determine the effect of this on power flow along the path. We consider the simplest example first to emphasize the concepts involved. 

In Section 2-7, we found from the ray-path equation of geometric optics, that there are certain rays within the core of a circular fiber which have an... 

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