Random system

Select from each of the following pairs the more random system. 

Automated randomization systems have been developed using voice response [44] and telephone touch-tone technology [45,46]. Others have used a preloaded password-protected system with hidden encrypted randomization files into the trial s laptop or desktop computers that are used as distributed data collection devices [47] or have developed centralized computer programs that dynamically randomize subjects [48]. 

Spence ER, Homey A. Automated telephone randomization system. Controlled Clin Trials 1999 20 2S 88S. 

No real system is fully random. Random systems are over-simplified ideal models similar to those of strictly regular structures. Most relevant is the effect of the finite volume of the monomer units which implies that two units can approach each other only up to their diameter. Thus a certain volume is forbidden or excluded for the individual repeating units. For hard sphere monomers this excluded volume is just eight times the monomer volume. This excluded volume... 

In short, Co was found to be 0.10, which is less than the value for a completely random system—which implies that the clusters were not randomly dispersed. A log—log plot of a versus C— Co was found to be linear where n, the slope of the line, was 1.5, which in fact is in the established theoretical range of 1.3-1.7. 

There have been few synthetic reports employing these monomers beyond the Ballard work, most likely as a result of presumed high cost and monomer availability. However, the performance and stability demonstrated by these materials in fuel cells may spur further developments in this area. The above-reported copolymers are believed to be random systems both in the chemical composition of the copolymer backbone and with regard to sulfonic acid attachment. Novel methods have been developed for the controlled polymerization of styrene-based monomers to form block copolymers. If one could create block systems with trifluorostyrene monomers, new morphologies and PEM properties with adequate stability in fuel cell systems might be possible, but the mechanical behavior would need to be demonstrated. 

Random Systems The scattering from random two-phase systems was considered by Debye(13,14) and other accounts are available (15,16) These formulations have been applied to gels of a fairly stiff polymer by Goebel, Berry and Tanner (17,18) If the system is spatially isotropic then ... 

Non-Random Systems. As pointed out by Cahn and Hilliard(10,11), phase separation in the thermodynamically unstable region may lead to a non-random morphology via spinodal decomposition. This model is especially convenient for discussing the development of phase separating systems. In the linearized Cahn-Hilliard approach, the free energy of an inhomogeneous binary mixture is taken as ... 

Random motion is ubiquitous. At the molecular level, the thermal motions of atoms and molecules are random. Further, motions in macroscopic systems are often described by random processes. For example, the motion of stirred coffee is a turbulent flow that can be characterized by random velocity components. Randomness means that the movement of an individual portion of the medium (i.e., a molecule, a water parcel, etc.) cannot be described deterministically. However, if we analyze the average effect of many individual random motions, we often end up with a simple macroscopic law that depicts the mean motion of the random system (see Box 18.1). 

A more intuitive definition of entropy is in terms of probability a more random system has higher probability and therefore higher entropy. 

From Eqs. (4.86)-(4.88) one finds that in a random system the linear part of the susceptibility obeys the superposition rule y = [y + 2y ]/3. Therefore the particle anisotropy drops out of the result. However, the cubic susceptibility appears to be rather sensitive to the anisotropy factor. Indeed, according to Eq. (4.88), for an assembly of magnetically rigid grains (S2 > 1), the susceptibility y(3), it is 3 times greater than that of an isotropic (S2 = 0) system. 

The other components, namely, b f and b j, may be constructed straightforwardly using their relations with the given ones [see Eqs. (4.192)]. For a random system, that is, for an assembly of noninteracting particles with a chaotic distribution of the anisotropy axes, the average of any Legendre polynomial is zero, so that b[1> = b, and the linear dynamic susceptibility reduces to... 

For a random system, the averages of Legendre polynomials drop out and = b. With respect to formalism constructed in Section III.A, these expressions yield the asymptotic representations for formulas (4.110) and (4.111) there. 

From Eq. (4.324), taking into account that for a solid random system the equilibrium statistical moments of the particle anisotropy axes are... 

Let us ask what the randomness that we associated with entropy in Chap. I means in terms of the assembly. A random system, or one of large entropy, is one in which the microscopic properties may be arranged in a great many different ways, all consistent with the same large-scale behavior. Many different assignments of velocity to individual molecules, for instance, can be consistent with the picture of a gas at high temperatures, while in contrast the assignment of velocity to molecules at the absolute zero is definitely fixed all the molecules are at rest. Then... 

Some of the examples shown in the following paragraphs present the characteristics of a random system with complete connections. However, other examples do not concern a completely connected system but present only some Markov unitary processes [4.6, 4.17]. 

Section 4.1, the group [(A,, u,P] defines a random system with complete... 

A complete particularization can be made in order to show more precisely that the case considered is a random system with complete connections. In this case, S is the first random vector ... 

Interactive Voice Response Randomization Systems Analytical Instrumentation SOP Management... 

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