Fibers defined

As follows from (3), sensor sensitivity is proportional to the sensor length L. In turn, as follows from (2), the maximal sensor length is limited by the absorption loss of a fiber. Defining / det(2) to be the power detection limit at which changes in the light intensity can still be detected reliably, the maximal sensor length allowed by the power detection limit can be calculated from (2) as ... 

Progress can be made by noting that electronic Hamiltonian (23) commutes with each of the A — 1 nuclear position variables. Think now of the molecular bound state space J as the square integrable sections in the trivial fiber bundle R3A 6 L2(R3N). In this case, the nuclear operator (which is the bare kinetic energy operator) acts in the base space, that is upon functions defined on R3A 6, and the electronic Hamiltonian acts only upon the fiber defined by the choice of b. (In this case, the fiber is a vector space and so the fiber bundle in this context is often called a vector bundle.) Now write the full electronic Hamiltonian as a direct integral over the fibers ... 

The requirement for TIR sets a limit on the angle of the light incident on the fiber that will be trapped in the core of the fiber. This condition is expressed in terms of the numerical aperture (NA) of the fiber, defined as the sine of the acceptance angle for incident radiation. 

Dtex Unit to measure the density of fibers, defined as the mass in grams per 1,000 m. Dtex = decitex = mass per 10,000 m... 

Modacrylic fibers (defined in the United States as those with 35-85% by weight acrylonitrile units) can be dissolved by more conventional solvents, such as acetone, and so were earlier on the market. Union Carbide introduced the first flame-resistant modacrylic fiber in 1948 imder the trade names Vinyon N and Dynel. Vinyon N was a continuous filament yarn Dynel was the staple form. Both were based on 60% vinyl chloride - 40% acrylonitrile copolymer. 

With a gel, the reptation model assumes that thermal diffusion occurs only along the tube axis as transverse motion is quickly stopped by the fibers defining the limits of the tube the ends of the chain can move freely, and they define new tube sections as the thermal motion along the tube axis forces them to enter new pores. 

The abihty of a waveguide to collect light is determined by the numerical aperture (NA) which defines the maximum angle at which light entering the fiber can be guided. 

A schematic stress-strain curve of an uncrimped, ideal textile fiber is shown in Figure 4. It is from curves such as these that the basic factors that define fiber mechanical properties are obtained. 

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

The abihty of a fiber to absorb energy during straining is measured by the area under the stress—strain curve. Within the proportional limit, ie, the linear region, this property is defined as toughness or work of mpture. For acetate and triacetate the work of mpture is essentially the same at 0.022 N/tex (0.25 gf/den). This is higher than for cotton (0.010 N/tex = 0.113 gf/den), similar to rayon and wool, but less than for nylon (0.076 N/tex = 0.86 gf/den) and silk (0.072 N/tex = 0.81 gf/den) (3). 

Olefin fibers, also called polyolefin fibers, are defined as manufactured fibers in which the fiber-forming substance is a synthetic polymer of at least 85 wt % ethylene, propjiene, or other olefin units (1). Several olefin polymers are capable of forming fibers, but only polypropylene [9003-07-0] (PP) and, to a much lesser extent, polyethylene [9002-88-4] (PE) are of practical importance. Olefin polymers are hydrophobic and resistant to most solvents. These properties impart resistance to staining, but cause the polymers to be essentially undyeable in an unmodified form. 

Twelve oxygen grades are defined by the Gas Specification Committee of the Compressed Gas Association (CGA) (24), 10 of which are given in Table 4. The contaminants identified relate to possible residues from the atmosphere as well as particulates or fibers that may have been contributed by the manufacturing process or the distribution system. In addition, government agencies and certain commercial users have developed specifications for individual needs (25). In most cases, these specifications closely parallel the CGA grades. 

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