Random array

Hashin and Rosen [3-8] extended Hashin s work to fiber-reinforced composite materiais. The fibers have a circular cross section and can be hoilow or solid. Two cases were treated (1) identical fibers in a he gotiaLarray and (2) fibers of various diameters (but same ratio of insldeto outside diameter, if hollow) in a random array. The two types of arrays are depicted in Figure 3-21. In both cases, the basic anaiysis... 

In the mid-1950s, alumina-silica catalysts, containing 25 percent alumina, came into use because of their higher stability. These synthetic catalysts were amorphous their structure consisted of a random array of silica and alumina, tetrahedrally connected. Some minor improvements in yields and selectivity were achieved by switching to catalysts such as magnesia-silica and alumina-zirconia-silica. 

Tomadakis, MM Sotirchos, SV, Transport Properties of Random Arrays of Freely Overlapping Cylinders with Various Orientation Distributions, Journal of Chemical Physics 98, 616, 1993. 

Alternatively, an assembly of microelectrodes can alleviate some of the problems associated with the individual microelectrodes. Such a random array of microelectrodes (RAM) comprises about 1000 carbon fibres (each of diameter 5-7 pm) which are embedded randomly within an inert adhesive such as an epoxy resin. (The ends of the fibres need to be widely spaced.) The net result is to generate an electrode system with a superior response time and a current which is IfKK) times that of a single microelectrode. By increasing the current in this way, the sensitivity of measurement is further increased. 

Random array of microelectrodes (RAM) A microelectrode system comprising about 1000 carbon fibres embedded randomly within an inert adhesive such as an epoxy resin. 

An isolated cs plane or a random array of cs planes, known as the Wadsley defect, still gives rise to nonstoichiometry. Regularly recurring cs planes result in a homologous series of stoichiometric intermediate phases. Occurrence of such equidistant cs planes in a crystal indicates a cooperative mechanism. The formula of a cs phase depends on the cs plane index as well as the width of the parent slab between cs planes. If MO is the formula of the parent line phase, the formula of the homologous series of oxides resulting from cs may be represented as where n is the width (number of... 

As we shall see below, for dilute solutions the electron is not attached to the alkali ion but is trapped in a cavity, around which the ammonia is polarized. The problem of the metal-insulator transition, then, is one of a random array of one-electron centres, as in a doped single-valley semiconductor. On the other hand, the disorder is less because the strong overlap between the wave functions of some pairs of centres characteristic of doped semiconductors is absent. In doped semiconductors there is no discontinuity in s2 at the transition. As explained in Chapter 5, this may be because of the very strong disorder or, in many-valley systems, because of self-compensation. In metal-ammonia solutions, as in the fluid alkali metals discussed in Section 4, both are absent. 

Ham [508] considered that the growth of a random array of precipitating particles could be approximated to a simple cubic lattice of spherical sinks of radius R to which more material diffused from the supersaturated solution. A model of the type is very similar to those models discussed by Reek and Prager [507] and Lebenhaft and Kapral [492], The analysis which Ham introduced highlights a similarity between the competitive effect and the Wigner—Seitz model of metals. 

The 0 s and l s represent different particles or spins depending upon the system being studied and their definition will be given below for different systems. The disordered state corresponds to a random array of 0 s and l s. The ordered state is described by an ordered arrangement of the 0 s and l s. The total number of lattice sites equals N. The number of 0 s and Us on the lattice are respectively no and m and n + no = A ... 

Effectiveness of catalytic archipelagos-II Random arrays of random islands (with D.-Y. Kuan and H.T. Davis). Chem. Eng. Sci. 38, 1569-1579 (1983). 

Intuitively, however, the RVE for an amorphous polymer may be expected to be no more than 10 nanometres or so. In an aligned fibre composite with continuous fibres we need to take a sample sufficiently large as to contain perhaps 30 to 50 fibres in a lateral dimension and in this case the coefficient of variation of stress as between fibres would enable a measure to be decided. In a random array of fibres however (chopped strand mat) the RVE must be of the order of a fibre length at least as is also the case for an aligned short fibre composite. 

The nature of the transition to the metallic state is not yet well understood, but it is useful at this stage to consider the arguments presented by Mott concerning this general problem (33). In a crystalline array of atoms, as the distance between the atoms is decreased a sharp transition to the metallic state is expected to occur. For a random array, the the transition sharpness is lost because of the disordered atomic arrangement. 

General atomic array Random arrays of atoms and molecules Arrays of atoms or molecules in regular patterns... 

One component system Atomic array Only one type of random array is possible. Many types of ordered arrays are possible. 

Then, why do Nichia s GaN lasers work at all The answer lies with two other serious non-uniformities present in the laser (1) an accidental non-uniformity within the quantum well due to spinodal decomposition [7], and (2) the intentional use of quantum wells and heterostructures to define sheets of high population inversion and photon confinement. The former effect creates a granulated, random array of InN-rich quantum boxes within the intended quantum well volume, which confine the population inversion within these nanoscopic regions of high optical quality. While the random... 

Kuan, R. Aris, and H. T. Davis, Effectiveness of Catalytic Archipelagos. II. Random Arrays of Random Islands, copyright 1983 [9], Pergamon Press PLC. 

Fig. 2. Schematic NMR spectra of arrays of protons (a) two protons (6) semi-isolated pairs of protons (c) a random or nearly random array of protons...

An isolated CS plane is referred to as a Wadsley defect and a random array of CS planes is considered to constitute planar (extended) defects which are entirely different from point defects. It is obvious that when CS planes occur at regular intervals, the composition of the crystal is stoichiometric, whereas a random array of CS planes results in nonstoichiometric compositions. While we have invoked anion vacancies which are later annihilated in our description of CS plane formation, we must point out that vacancies are not essential precursors for the formation of CS planes. Accommodating anion-deficient nonstoichiometry through CS mechanism is a special feature restricted to d° metal oxides such as W03, Nb205 and TiOz which exhibit soft phonon modes. Soft phonon modes in metal oxides arise from soft metal-orxygen potentials which permit large cation relaxation. The latter... 

Electrode geometry — Figure 2. Array geometries, a Random array of inlaid disk electrodes b ordered array of inlaid disk electrodes c double band array d interdigitated array... 

For these reasons we turned first to a version of seriation that had no specific spatial task requirement only a search one. Using computer driven touch screens, we displayed a variety of icons varying in size in random linear arrays, and required that subjects touch each one once only, according to a sequential rule such as biggest to smallest. The randomized arrays ensured that there was no correlation between the way the sizes appeared, and (e.g.) the monotonic search path that had to be complied with (see Figure 10.5a). In this way, we have been able to assess size seriation, considered as an extended serial search task without manipulation requirements and spatial confounds. 

---