Tests temporal scale

As it is known [12], the elasticity modulus E value in polymiers impact tests grows at testing temporal scale decrease (at brittle fracture - time up to failure and can be described according to the empirical relationship [12] ... 

Since (p j depends on strain rate (testing temporal scale) then the indicated structural parameter is dependent on the time order parameter and for it one can write [23] ... 

In Fig. 3.4, the comparison of experimental and calculated according to the Eq. (3.13) values tp j and respectively, is adduced, which shows their good correspondence. This means, that at impact loading of HOPE with de-vitrificated amorphous phase a its definite part mechanical vitrification occurs, the fraction of which increases at testing temporal scale reduction [21 ]. 

Let us consider in the present chapter conclusion the treatment of dependences of yield stress on strain rate and crystalline phase structure for semicrystalline polymers [77]. As it known [91], the clusters relative fraction is an order parameter of polymers structure in strict physical significance of this term and since the local order was postulated as having thermofluctuation origin, then cp, should be a function of testing temporal scale in virtue of... 

Having determined value t as duration of linear part of diagram load -time P -1) in impact tests and accepting is equal to clusters relative fraction in quasistatic tensile tests [92], the values (p, (r) can be estimated. In Fig. 4.22, the dependences on strain rate for HOPE and polypropylene (PP) are shovm, which demonstrate increase at strain rate growth, that is, tests temporal scale decrease. 

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... 

Comparisons of SED-TOX scores are only meaningful when made between sediment samples collected at the same time and evaluated with the same toxicity tests this is however not always possible. Therefore, the effects of inconsistency in test selection and in the temporal scale of sediment sampling on the SED-TOX scores has to be established. 

The different relaxation processes proceeding degree for three types of tests, which is due to different temporal scale, is the cause of elasticity modulus such behavior. These processes, as it was to be expected, are realized in loosely packed matrix (more in detail see chapter two). The higher the indicated relaxation degree is (relaxation processes completion) the smaller value is. This allows to approximate the obtained empirically linear correlations E D) by the common for all three tests types relationship [1] ... 

This chapter has proposed alternative functional forms to describe the viscoelastic functions. The two previous sections made direct tests of the validity of these forms. The functional forms predicted by the temporal scaling ansatz describe accurately the experimental measurements, once appropriate material-dependent parameters are chosen. Equivalently, the curve-fitting process reduced each set of measurements of G (a>), G" co), or 7(/c) to a small number of system-dependent parameters. 

Literature studies were not planned as tests for the temporal scaling ansatz. Unsurprisingly, all studies are not equally helpful in the discussion below. The most useful experiments were conducted on one polymer system at a substantial number of concentrations, or at one concentration for homologous polymers having a substantial number of molecular weights. 

Figure 13.39 Test of the Kronig-Kramers relations. G t) is calculated from Eqs. 13.16 and 13.17, using the temporal scaling ansatz functional forms as fitted to data from Colby, et a/. (15) to represent G and G". Solid and dashed lines represent, respectively, G t) from G and from G", for polybutadiene in phenyloctane at volume fractions (top to bottom) 1.00,0.49,0.28,0.14,0.062, and 0.027.

In situ measurements of stratospheric reactive trace gas abundances provide an opportunity to test the fundamental photochemical mechanisms (3). The advantage of such measurements is that they are local, so the simultaneous measurements of trace gases place a true constraint on the possible photochemical mechanisms. These measurements are also able to resolve small-scale spatial and temporal structure in the trace constituent fields. The disadvantage of in situ measurements is that they do not capture the global or perhaps even seasonal view of photochemical transformations because they are seldom done frequently enough or in enough places to provide that information. Another disadvantage of in situ measurements is that they must be made from platforms in the stratosphere, and these remote observational outposts have their liabilities. 

Pupil size can be estimated from direct observation. A variety of cards and scales are available whereby the experimenter compares the size of the pupil to standard patterns and scales. The simplest and most often used card is the Haab pupil gauge. This consists of a card with black circles graduated in size between 2 and 10 mm in 0.5-mm increments. The card is held on the temporal side of the eye out of the subject s vision (to reduce accommodation miosis). Pupil size can be determined to an accuracy of 0.2 mm. A disadvantage of this method is the inability to make measurements in the dark and the possibility that the subject s eyes will react to the test or its administration. 

In contrast, the asymptotic approach puts minimal strain on the computer but demands more of the modeller. The convergence of the computed solutions is usually easy to test with respect to spatial and temporal resolution, but situations exist where reducing the timestep can make an asymptotic treatment of a "stiff" phenomenon less accurate rather than more accurate. This follows because the disparity of time scales between fast and slow phenomena is often exploited in the asymptotic approach rather than tolerated. Furthermore, the non-convergence of any particular solution is often easier to spot in timestep splitting with asymptotics because the manner of degradation is usually catastrophic. In kinetics calculations, lack of conservation of mass or atoms signals inaccuracy rather clearly. 

The results provided by three-dimensional MRTM are consistent with the numerical output of one-dimensional MRTM. The concentration-depth curves are shown to be similar for a nominal test case that is independent of temporal and spatial scales. Besides the numerical output that the model generates, the visualization component of the model gives an almost instantaneous look into the spatial distribution of the contaminant. This visualization is made by sliding three planes (horizontal, longitudinal, and transversal) across the entire simulation domain. Concentrations are scaled from 0.0 to the maximum values so that the trace concentrations can be easily visualized. The numerical value of the maximum concentration is also output in the visualization window, together with the current position of the visualization plane. When the trace compound is hazardous (e.g., a heavy metal such as mercury), it is also necessary to monitor the spatial distribution of very low concentrations. The current three-dimensional, MRTM visualization method provides the means to track these types of trace concentrations. 

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