Reduced-time scaling factors

In Eq. (20), e(t) represents uniaxial kinematic strain at current time t, cr(t) is the Cauchy stress at time t is the elastic compliance and D (vl ) is a transient creep compliance function. The factor defines stress and temperature effects on elastic compliance and is a measure of state-dependent reduction (or increase) in stiffness, gQ = g ia, ). The transient (or creep) compliance factor g has similar meaning, operating on the creep compliance component. The factor g2 accounts for the influence of load rate on creep, and depends on stress and temperature. The function represents a reduced time-scale parameter defined by... 

Let say we have a high order transfer function that has been factored into partial fractions. If there is a large enough difference in the time constants of individual terms, we may try to throw away the small time scale terms and retain the ones with dominant poles (large time constants). This is our reduced-order model approximation. From Fig. E3.3, we also need to add a time delay in this approximation. The extreme of this idea is to use a first order with dead time function. It obviously cannot do an adequate job in many circumstances. Nevertheless, this simple... 

Photoionization and therefore EXAFS takes place on a time scale that is much shorter than that of atomic motions so the experiment samples an average configuration of the neighbors around the absorber. Therefore, we need to consider the effects of thermal vibration and static disorder, both of which will have the effect of reducing the EXAFS amplitude. These effects are considered in the so-called Debye-Waller factor which is included as... 

For AEGL-3, the 1-h LC50 of 82 ppm for squirrel monkeys (Haun et al. 1970) was reduced by a factor of 3 to estimate a lethality threshold (27.3 ppm). Temporal scaling to obtain time-specific AEGL values was described by C% t=k (where C=exposure concentration, t=exposure duration, and k=a constant). The lethality data for the species tested indicated a near linear relationship between concentration and exposure duration (n=0.97 and 0.99 for monkeys and dogs, respectively). The derived exposure value was adjusted by a total uncertainty factor of 10.2 An uncertainty factor of 3 was applied for... 

LES/FDF-approach. An In situ Adaptive Tabulation (ISAT) technique (due to Pope) was used to greatly reduce (by a factor of 5) the CPU time needed to solve the set of stiff differential equations describing the fast LDPE kinetics. Fig. 17 shows some of the results of interest the occurrence of hot spots in the tubular LDPE reactor provided with some feed pipe through which the initiator (peroxide) is supplied. The 2004-simulations were carried out on 34 CPU s (3 GHz) with 34 GB shared memory, but still required 34 h per macroflow time scale they served as a demo of the method. The 2006-simulations then demonstrated the impact of installing mixing promoters and of varying the inlet temperature of the initiator added. 

The scaling the functional shape hardly depends on temperature. Curves corresponding to different temperatures superimpose in a single master curve when they are represented against a reduced time variable that includes a T-dependent shift factor. 

Due to the existence of two quite different distinctive distances (scale factors) - lo and l - the recombination kinetics also reveals two stages called monomolecular and bimolecular respectively. The defects survived in their geminate pairs go away, separate and start to mix and recombine with dissimilar components from other pairs. It is clear that the problem of kinetics of the monomolecular process is reduced to the time development of the probability w(f) to find any single geminate pair AB as a function of the initial spatial distribution of the pair components f(r), recombination law cr(r) and interaction Uab (r). The smaller the initial concentration of defects, n(0) —> 0, as lo —> oo, the more correct is the separation of the kinetics into two substages, whereas the treatment of the case of semi-mixed geminate pairs is a very difficult problem discussed below. 

---