Dynamic scaling law

The molecular properties H t), determined by the minor chain model (Table 1), are interrelated and have a convenient common scaling law. The dynamic proper-... 

The relaxation time in Eq. (15) and the scaling law Z — 2v+ for the dynamic critical exponent Z are then understood by the condition that the coil is relaxed when its center of mass has diffused over its own size... 

Special theoretical insight into the internal relaxation behavior of polymers can also be provided on the basis of dynamic scaling laws [4,5]. The predictions are, however, limited since only general functional relations without the corresponding numerical prefactors are obtained. 

Sikorsky and Romiszowski [172,173] have recently presented a dynamic MC study of a three-arm star chain on a simple cubic lattice. The quadratic displacement of single beads was analyzed in this investigation. It essentially agrees with the predictions of the Rouse theory [21], with an initial t scale, followed by a broad crossover and a subsequent t dependence. The center of masses displacement yields the self-diffusion coefficient, compatible with the Rouse behavior, Eqs. (27) and (36). The time-correlation function of the end-to-end vector follows the expected dependence with chain length in the EV regime without HI consistent with the simulation model, i.e., the relaxation time is proportional to l i+2v The same scaling law is obtained for the correlation of the angle formed by two arms. Therefore, the model seems to reproduce adequately the main features for the dynamics of star chains, as expected from the Rouse theory. A sim-... 

One must bear in mind that the parameter a describes the scaling law (75) for the temporal variable and is equal to the inverse dynamic fractal dimension ex = 1 /Dd- Thus, the dynamic HSR (84) can be rewritten as... 

Note that the dynamic fractal dimension obtained on the basis of the temporal scaling law should not necessarily have a value equal to that of the static percolation. We shall show here that in order to establish a relationship between the static and dynamic fractal dimensions, we must go beyond relationships (83) and (84) for the scaling exponents. 

ANALYSIS - SCALING LAWS COMPUTER CODES - BLAST SUPPRESSION DYNAMIC STRESS ANALYSIS - STRUCTURES FABRICATION AND TESTING COST EFFECTIVENESS ANALYSIS ENGINEERING SUPPORT... 

Pumps that follow the above relations are called similar or homologous pumps. In particular, when the n variable C, which involves force are equal in the series of pumps, the pumps are said to be dynamically similar. When the 11 variable Cq, which relates only to the motion of the fluid are equal in the series of pumps, the pumps are said to be kinematically similar. Finally, when corresponding parts of the pumps are proportional, the pumps are said to be geometrically similar. The relationships of Eqs. (4.30) and (4.31) are called similarity, affinity, or scaling laws. 

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