Principle, equivalence

We shall presently examine the physical significance of the shift factors, since they quantitatively embody the time-temperature equivalence principle. For the present, however, we shall regard these as purely empirical parameters. The following Ust enumerates some pertinent properties of a ... 

Mossbauer resonance of Zn to study the influence of the gravitational field on electromagnetic radiation. A Ga ZnO source (4.2 K) was used at a distance of 1 m from an enriched ZnO absorber (4.2 K). A red shift of the photons by about 5% of the width of the resonance line was observed. The corresponding shift with Fe as Mossbauer isotope would be only 0.01%. The result is in accordance with Einstein s equivalence principle. Further gravitational red shift experiments using the 93.3 keV Mossbauer resonance of Zn were performed later employing a superconducting quantum interference device-based displacement sensor to detect the tiny Doppler motion of the source [66, 67]. 

Equivalence Principle. The conformation of a polymer chain in the crystalline state is defined by a succession of equivalent structural units which occupy geometrically (not necessarily crystallographically) equivalent positions with respect to the chain axis. The chain axis is parallel to a crystallographic axis of the crystal. 

Principle of Minimum Internal Conformational Energy. The conformation of a polymer chain in a crystal approaches one of the minima of the internal conformational energy, which would be taken by an isolated chain subjected to the restrictions imposed by the equivalence principle. 

Polymers showing crystalline mesomorphic modifications, characterized by chains in disordered conformations, are exceptions to the equivalence principle. Examples of these cases are shown in Section 2.6. 

Figure 2.4 Line repetition symmetries, according to equivalence principle, and corresponding possible conformations, according to minimum conformational energy, for (a) isotactic and (b) syndiotactic polypropylene (T = trans, G = gauche).

In the case of syndiotactic polypropylene (sPP), the configuration corresponds to an alternating succession of couples of (+), (+) and (—), (—) bonds (Figure 2Ab). If 0i and 02 are the torsion angles of two successive bonds of the chain, the equivalence principle imposes that the only possible successions of torsion angles are those shown in Figure 2.4b, 01 ... 

Calculations of the conformational energy are performed according to the equivalence principle and, as a consequence, a succession of backbone torsion angles. .. 0i020i 20i 2- is generally assumed for isotactic polymers. 

As discussed in Section 1, general requirements for the crystallizability of polymers are the regularity of the chemical constitution and of the configuration of long sequences of monomeric units. In these conditions the conformation of the chains is also regular (equivalence principle). However, some three-dimensional long-range (crystalline) order may be maintained even when disorder is present in the conformation of the polymer chains. 

An interesting consequence of the existence of 5th dimension is that in the 4 dimensional observations an apparent violation of the equivalence principle must appear as one can show it by writing the geodesic equation in 5 dimensions and then projecting it into 4 dimensions. Without going into details, the sign of p5 causes the appearance of a pseudo-charge q in the 4 dimensional formalism,... 

Tanaka, Chatani, and Tadokoro improved this model by refining the crystal structure of polyisobutene (182). The resulting structure is a 2/1 helix in which the structural unit contains four nonequivalent monomer units. In the crystal cell there are always eight monomer units arranged in three turns but the 8/3 helical symmetry is no longer retained. This example represents one of the most notable exceptions to the equivalence principle. Displacement from the exact helical conformation is small, however, and all the pairs of torsion angles fall inside the same energy well. 

All aspects of the electronic records and electronic signature systems in place have been designed to provide a level of security and control equal to or exceeding the equivalent controls inherent to manual (paper) systems. This equivalency principle provides evaluative criteria for all electronic signatures. There is not a mandate to make a system perfect, error-free, or completely hacker-proof, although these are all appropriate ultimate goals rather, sufficient controls are required to assure that an electronic system is as secure or more secure than an equivalent manual system. 

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

First, and as already noted, the model universe is populated exclusively by primitive particles that possess solely the property of enumeration, and hence quantification. Consequently, all motions in the model universe are effectively gravitational, and we model this circumstance by constraining all such motions to satisfy the weak equivalence principle, by which we mean that the trajectory of a body is independent of its internal constitution. This constraint can be expressed as follows ... 

The recent advances in producing, trapping and cooling antiprotons and positrons opened the possibility of antihydrogen formation in laboratory. This may allow the studies of antimatter and tests of fundamental physical principles such as charge - parity - time ( CPT ) invariance or the weak equivalence principle (WEP) for antiparticles. Such experiments are planned at the newly built CERN AD (Antiproton Decelerator) within ASACUSA, ATRAP and ATHENA projects, which have just started their operations. 

It is well established that between Tg and about Tg + 50 K, the relaxation kinetics obeys the WLF law (Williams et al., 1955). If Pr is a property depending on the macromolecular mobility (relaxation modulus, complex modulus, viscosity, diffusion rate, etc.), the time-temperature equivalence principle may be formulated as... 

It was initially stated that Cf are Cf were universal constants (Cf 17 Cf 50 K), but Cf can vary between 2 and 50 and Cf between 14 and 250 K (Mark, 1996). Epoxy values have been found in the low part of these intervals Cf 10, Cf 40 15 K (Gerard et al., 1991), whereas unsaturated polyester values can be relatively high Cf/Cf = 15-55 = 73-267 K (Shibayama and Suzuki, 1965). There is, to our knowledge, no synthetic study on the ideality and crosslinking effects on Cfand Cf. The time-temperature equivalence principles will be examined in detail in Chapter 11, which is devoted to elasticity and viscoelasticity. 

As discussed in Chapter 10, network polymers - as linear polymers - obey the time-temperature equivalence principle in the domain where they are stable, both chemically (no postcure, no thermal degradation), and physically (no orientation relaxation, water desorption, physical aging, etc.). 

From a time-temperature equivalence principle (see below), any material history may be represented by an isothermal equivalent, corresponding to a point U (tu, Tu) in the (t, T) graph. If the point U is below the TSC curve, the material will not undergo failure in the particular conditions. In contrast, if the point U is above the TSC curve, the material will undergo failure because its index % will change sign. 

Hughes, R.J. (1993b). The equivalence principle. Contemporary Physics 34 177-191. 

Indications for surgical intervention include regurgitation with NYHA lll-IV symptoms or NHYA >11 with atrial fibrillation refractory to conservative treatment. Several surgical techniques are effective, The Alfieri stitch or edge to edge technique is of interest because one of the percutaneous mitral valve repair techniques is based on an equivalent principle (29,30). Currently two methods for transcatheter mitral valve repair are investigated in clinical trials ... 

---