Linear sizes

Defect s indication of linear size W (and larger) are forming above such the cracks, the width of which satisfies the inequality... 

Note - In designing a system based on the settling velocity of nonspherical particles, the linear size in the Reynolds number definition is taken to be the equivalent diameter of a sphere, d, which is equal to a sphere diameter having the same volume as the particle. 

The total resistance is the sum of friction and eddy resistances. Both factors act simultaneously, but their contribution in the total resistance depends on the conditions of the flow in the vicinity of the particle. Hence, for the most general case the resistance force is a function of velocity, w, density, p, viscosity, the linear size of a particle, C, and its shape, ijr. Thus,... 

Zorbax PSM Bimodal and Trimodal columns are packed with mixed pore-size packing to achieve linear size separations over a broad molecular weight range (Table 3.3). Zorbax PSM Bimodal columns are packed with PSM 60 and PSM 1000 particles, and Trimodal columns contain PSM 60, PSM 300, and PSM 3000 particles (Fig. 3.4). Carefully selecting and mixing different pore-size particles in columns provide much better linearity than coupling columns that are each packed with single pore-size particles. 

As a rule, the dispersed catalysts are polydisperse (i.e., contain crystallites and/or crystalline aggregates of different sizes and shapes). For particles of irregular shape, the concept of (linear) size is indehnite. For such a particle, the diameter d of a sphere of the same volume or number of metal atoms may serve as a measure of particle size. 

Fig.2 Melting temperatures of polymers (faTm/Ec) with variable chain lengths. The solid line is calculated from Eq. 10, the dashed line is calculated from Flory-Vrij analysis (Eq. 11), and the circles are the simulation results in the optimized approach. In simulations, the occupation density is 0.9375, and the linear size of the cubic box is set to 32 for short chains and 64 for long chains (Hu and Frenkel, unpublished results)...

Fig. 8 Theoretical liquid-liquid demixing curve (solid line) and the bulk melting temperature (dashed line) of a flexible-polymer blend with one component crystallizable and with athermal mixing. The chain lengths are uniform and are 128 units, the linear size of the cubic box is 64, and the occupation density is 0.9375 [86]...

In contrast, a linear size-consistent (Zmax + )-3 extrapolation of just the MP2/cc-pVTZ and MP2/cc-pVQZ energies is accurate to 0.63 kcal/mol (Table 4.4). If we try to further reduce the basis sets to cc-pVDZ and cc-pVTZ, the error in the extrapolation increases to 6.0 kcal/mol. However, the new double extrapolation provides the complete basis set MP2 limit with an absolute accuracy of 0.86 kcal/mol without recourse to basis sets larger than cc-pVTZ [4s3p2dlf/3s2pld] (Table 4.6). 

Figure 3. Effect of solvent on the effective linear sizes of molecules in solution (Fuel 1982) (14) ...

The number of inputs which are available for controlling crystallisation processes is limited. Possible Inputs for a continuous evaporative crystallisation process are, crystalliser temperature, residence time and rate of evaporation. These Inputs affect the crystal size distribution (CSD) through overall changes in the nucleatlon rate, the number of new crystals per unit time, and the growth rate, the increase in linear size per unit time, and therefore do not discriminate directly with respect to size. Moreover, it has been observed that, for a 970 litre continuous crystalliser, the effect of the residence time and the production rate is limited. Size classification, on the other hand, does allow direct manipulation of the CSD. 

Note Hard-segment phase domains are typically of 2-15 nm linear size. 

A large stockpile of coal is burning. Every part of its surface is in flames. In a 24-hr period the linear size of the pile, as measured by its silhouette against the horizon, seems to decrease by about 5%. 

The separation of chemical species by size exclusion chromatography is more reproducible than any other type of chromatography. Once the SEC columns, the mobile phase (most often a pure solvent like THF or toluene), and the flow rate are selected, the retention volume (or retention time assuming the flow rate does not change) is primarily a function of linear molecular size, which can be obtained from the valence bond structure if the compound is known. Some of the chemical species can interact with the solvent forming complexes with an effective linear size greater than that of the molecule. This causes the expected retention volume, based on "free" molecular structure, to shift to a lower but very reproducible retention volume. Phenols in coal liquids form 1 1 complex with THF (9,10) and carry the effective linear molecular size to increase. As a result phenolic species elute sooner than expected from their... 

Preliminaries. In this chapter we shall address the simplest nonequilibrium situation—one-dimensional locally electro-neutral electrodiffusion of ions in the absence of an electric current. We shall deal with macroscopic objects, such as solution layers, ion-exchangers, ion-exchange membranes with a minimum linear size of the order of tens of microns. 

In recent years investigations were begun in which the variation of adsorbent properties, such as electrical conductivity (1, 2), dielectric permeability (3-5), and linear sizes (6-11), were studied. In these systems the adsorbents were usually active carbons and porous glasses. Only a few studies were carried out on zeolites these studies are interesting because of the perfect porous structures (12-14) of zeolites. All these studies showed that during adsorption the properties of adsorbents do not remain constant. 

For the long reaction times, Id Ao, this new scale dominates over all other dimensions of the process and thus we can consider a model where the whole reaction volume is divided into such alternating blocks with linear sizes Id, and each of them contains either A or B particles predominantly (Fig. 2.8). 

Calculation done by Schroder and Eberlein [3, 83], has shown than even for small recombination regions, e,g., that containing only nearest to a vacancy sites in the b.c.c. lattice, Rett 0.81ao which very close to the linear size of the recombination region, Rmax = ao /3/4 0.866ao. 

The whole reaction volume at long times may be qualitatively considered as consisting of domains with the linear size , each domain has particles of one kind only, A or B. Particles A are distributed inside such domains randomly (which follows from the fact that X (r,t) const, as r < ). In... 

At longer times, when re , the effect of the statistical aggregation of similar particles begins to dominate, which takes also place for neutral non-interacting particles as it was discussed in Chapter 5. At this stage the reaction leads to the formation of A- or B-rich domains with the linear size in turn, these domains are structured inside themselves into smaller blocks having the typical size of re, which however no longer affects the kinetics. 

In order to construct the expression for the equilibrium number of nuclei in a unit volume (the dimension of b(x)dx is cm-3, the dimension of b(x), when x is defined as the radius, is cm-2), we must multiply the exponent exp(- /fcT), where is determined by (17), by a quantity of dimension cm-2. Exact evaluation of a pre-exponential factor is presently an unsolved problem of statistical mechanics. Erom dimensional considerations we may propose d 2 or x 2, where d is the linear size of a molecule of liquid and x is the radius of a bubble. In the present problem of evaluating the critical (i.e., minimum) value of the equilibrium concentration, we are dealing with a region where the factor in the exponent is large and exact evaluation of the pre-exponential factor is not actually necessary. 

A conscious choice of such elements can be made but in general the equilibrium distribution of stress cannot be found except for particular geometries. The assumptions of uniform strain throughout the assembly or of uniform stress were respectively made by Voigt and by Reuss. Returning to the structures actually perceivable in polymers one may consider the spherulite in a semi crystalline polymer as being unsuitable as a RVE because the boundary is not included. However, an assembly of spherulites would be acceptable, since it would contain sufficient to make it entirely typical of the bulk and because such an assembly would have moduli independent of the surface tractions and displacements. The linear size of such a representative volume element of spherulites would be perhaps several hundred microns. 

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