Stretching factor

Here, a is a stretched factor, and Xdark is the characteristic time of the non-radiative relaxation. 

In Section 29.3 it has been shown that a matrix generates two dual spaces a row-space S" in which the p columns of the matrix are represented as a pattern P , and a column-space S in which the n rows are represented as a pattern P". Separate weighted metrics for row-space and column-space can be defined by the corresponding metric matrices and W. This results into the complementary weighted spaces and S, each of which can be represented by stretched coordinate axes using the stretching factors in -J v and, where the vectors w and Wp contain the main diagonal elements of W and W. ... 

Fig. 8 Effective stretching factor y = (Ze(pa)/Ze(0)> as obtained a within the simulation as a function of the scaled anchoring density /RvY and b from the self-consistent...

Knitted nets are produced from blown film or specialized extmsion lines with corotating dies. The film rolls are slit into small tapes of 2-5 mm width. Then the tapes are stretched on heated rolls (galettes) in several steps to achieve and maintain a high level of orientation. Typical stretching factors are three to five times. Thus, the materiel undergoes a strain-induced crystallization, which maximizes the crystallinity level in the tape. 

Although the repeated application of the SAR principle leads to a highly regular lamellae pattern, it also exhibits an exponential increase in interfacial area [7]. The corresponding stretching factor is given by... 

P 62] A Lagrangian particle tracking technique, i.e. the computation of trajectories of massless tracer particles, which allows the computation of interfacial stretching factors, was coupled to CFD simulation [47]. Some calculations concerning the residence time distribution were also performed. A constant, uniform velocity and pressure were applied at the inlet and outlet, respectively. The existence of a fully developed flow without any noticeable effect of the inlet and outlet boundaries was assured by inspection of the computed flow fields obtained in the third mixer segment for all Reynolds numbers under study. 

Two strategies of particle tracking were used. As a first strategy, tracers were distributed along the interface of the two fluids (virtual, since miscible) for computation of interfacial stretching factors [47]. Then an iterative method for computing interfacial stretching was established. 

Figure 1.148 Interface stretching factor vs. element number for different Dean numbers ( ) K = 10 (A) K = 100 ( ) K = 200 [47],...

Using this graph and the relationship it contains, one can now address the question of whether and under what conditions a laminar flame can exist in a turbulent flow. As before, if allowance is made for flame front curvature effects, a laminar flame can be considered stable to a disturbance of sufficiently short wavelength however, intense shear can lead to extinction. From solutions of the laminar flame equations in an imposed shear flow, Klimov [44] and Williams [45] showed that a conventional propagating flame may exist only if the stretch factor K2 is less than a critical value of unity. Modeling the area change term in the... 

Figure 4.24 Schematic "phase diagram" for AB linear diblock molecules as a function of the molecular composition and the stretch factor, p.

This (2 X 2) notation can be generalized. First, it can take on the form m x n), where the numbers m and n are two independent stretch factors for the two unit cell vectors. These numbers are often integers, but need not... 

The tolerances for bond-stretch and angle-bend constraints are usually expressed as multiples of the constraint bond-stretch and bond-angle values, respectively (st) = (sf) X B, and (at) = (af) X , where (sf) is the stretch factor or relative bond-stretch tolerance and (af) is the angle-bend factor or relative angle-bend tolerance. Substitution of the tolerance expressions into Eq. [118] yields an analogous relation between the tolerance factors ... 

Spin stretch factor Tex per filament Tenacity Elongation (%) Initial modulus Orientation angle... 

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