Break expression

Enter a break expression in the Add Watch dialog box (see "Examining the Values of Variables" later in this chapter). 

Conditional break expression (break occurs when expression is True)... 

Tenacity. It is the stress at which the fiber breaks, expressed in grams per denier. It is a very important property of polyolefin fibers, and it can range between 3.5 and 8 g/d (grams per denier) or 31-81 g/tex [10]. General textile use PP fibers can have a tenacity of 40.5-50 cN/dtex, whereas high tenacity yams used in ropes and nets can have tenacities up to 81 cN/dtex [11]. 

The elongation of a specimen at break expressed as a percentage of the original length. 

As discussed above, elongation at break was severely compromised by the addition of glass fibers elongation values for the composite blends are adequately represented by a mean value standard deviation. This result is based on the ANOVA, which shows that approximately 98% of the data variability is due to the mean value hence, elongation at break (expressed in %) is stated as 3.43 0.45. However, for the compatibilized blend. Fig. 5.7c shows the response surface at the lowest shear rate (corresponding to a screw speed of 300 rpm). All of these values were in excess of 30% elongation. As reported in a previous publication (61), elongation increased with increased shear rate for the compatibilized blend. 

The ultimate elongation is a measure of how far a material will stretch before breaking, expressed as a percentage of its original length. 

There are some apparatus and methodical limitations in the HMOR measurement. The MOR is defined as the maximum stress a rectangular test piece of specific dimensions can withstand in a three-point bending test until it breaks, expressed in N/mm or MPa. Test piece dimensions are 150 mm x 25 mm x 25 mm. 

Another immediate application of r-RESPA is to the case when the force can be subdivided into a short range part and a long range part. One way for effectuating this break up is to introduce a switching function, s x) that is unity at short inter-particle separations and 0 at large inter-particle separations. We introduced this strategy in our earlier non-reversible RESPA paper [15] where we expressed the total force as. 

An R-matrix expresses the bond and electron rearrangement in a reaction. The R-matrix of Figure 3-12 reflects a reaction scheme, the breaking and the making... 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

Definitions of the commonly measured tensile properties are as follows Unear density (tex) is the weight in grams of 1000 m of yam. Tenacity is the tensile stress at break and is expressed in force-per-unit linear density of unstrained specimen, N /tex. Knot tenacity is the tensile stress required to mpture a single strand of yam with an overhand knot tied in the segment of sample between the testing clamps. It is expressed as force-per-unit linear density and is an approximate measure of the britdeness of the yam. Toop tenacity is the tensile stress required to mpture yam when one strand of yam is looped through... 

Duetility (ASTMD113). The ductihty of an asphalt is expressed as the distance in cm which a standard briquet can be elongated before breaking. Ductihty is a combination of dow properties and redects both cohesion and shear susceptibiUty. 

Statistical errors of dynamic properties could be expressed by breaking a simulation up into multiple blocks, taking the average from each block, and using those values for statistical analysis. In principle, a block analysis of dynamic properties could be carried out in much the same way as that applied to a static average. However, the block lengths would have to be substantial to make a reasonably accurate estimate of the errors. This approach is based on the assumption that each block is an independent sample. 

The most remarkable feature of expression (4.8) is that it does not contain any cross terms 8x 8s. This is a consequence of time-shift invariance of the instanton solution (d s/dt = dVjds, x = 0). This fact can be expressed as invariance of the action with respect to the infinitesimal transformation s s -I- cs, c 0 [cf. eq. (3.42)]. In the new coordinates the determinants break up into longitudinal and transverse parts and (4.4) becomes... 

At low temperatures, when the bath is quantum (icoj P 1), the rate expression, expanded in series over the coupling strength, breaks up into the contributions from the various processes involving the bath phonons... 

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