Discrete fines

This modified density Is a more slowly varying function of x than the density. The domain of Interest, 0 < x < h, Is discretized uniformly and the trapezoidal rule Is used to evaluate the Integrals In Equations 8 and 9. This results In a system of nonlinear, coupled, algebraic equations for the nodal values of n and n. Newton s method Is used to solve for n and n simultaneously. The domain Is discretized finely enough so that the solution changes negligibly with further refinement. A mesh size of 0.05a was adopted In our calculations. 

Unlike calcite and dolomite, siderite rarely forms as an extensive pore-filling cement, but rather as discrete fine crystals, spherules and nodules scattered in the host sediments. Nevertheless, Baker et al. (1996) found that early diagenetic siderite concretions (0.5-2 mm) form up to 30% of Triassic sandstones and mudstones from eastern Australia. Laterally continuous siderite-cemented offshore shelf sandstone sheets (15 cm thick) occur in Upper Cretaceous sequences from Canada (McKay et ai, 1995). 

Dispersing agent n. A material added, usually in relatively small percentage, to a suspending medium to promote and maintain the separation of discrete, fine particles of sohds or hquids. Dispersants are used, for example, in the wet grinding of pigments and for suspending water-insoluble dyes. 

Artiga Gonzales, R. A. et al., inventor, WO 2005/085410 Particles comprising discrete fine-particulate surfactant particles, Henkel, 2005. 

Fibrillated Fibers. Instead of extmding cellulose acetate into a continuous fiber, discrete, pulp-like agglomerates of fine, individual fibrils, called fibrets or fibrids, can be produced by rapid precipitation with an attenuating coagulation fluid. The individual fibers have diameters of 0.5 to 5.0 ]lni and lengths of 20 to 200 )Jm (Fig. 10). The surface area of the fibrillated fibers are about 20 m /g, about 60—80 times that of standard textile fibers. These materials are very hydrophilic an 85% moisture content has the appearance of a dry soHd (72). One appHcation is in a paper stmcture where their fine fiber size and branched stmcture allows mechanical entrapment of small particles. The fibers can also be loaded with particles to enhance some desired performance such as enhanced opacity for papers. When filled with metal particles it was suggested they be used as a radar screen in aerial warfare (73). 

Quality Control. Because fine chemicals are sold according to specifications, adherence to constant and strict specifications, at risk because of the batchwise production and the use of the same equipment for different products ia multipurpose plants, is a necessity for fine chemical companies. For the majority of the fine chemicals, the degree of attention devoted to quahty control (qv) is not at the discretion of the iadividual company. This is particularly the case for fine chemicals used as active iagredients ia dmgs and foodstuffs (see Fine chemicals, standards). Standards for dmgs are pubHshed ia the United States Pharmacopeia (USP) ia the United States (6) and the European Pharmacopeia ia Europe (7). 

The raw ROM (run of mine) ore is reduced in size from boulders of up to 100 cm in diameter to about 0.5 cm using jaw cmshers as weU as cone, gyratory, or roU-type equipment. The cmshed product is further pulverized using rod mills and ball mills, bringing particle sizes to finer than about 65 mesh (230 p.m). These size reduction (qv) procedures are collectively known as comminution processes. Their primary objective is to generate mineral grains that are discrete and Hberated from one another (11). Liberation is essential for the exploitation of individual mineral properties in the separation process. At the same time, particles at such fine sizes can be more readily buoyed to the top of the flotation ceU by air bubbles that adhere to them. 

Umestone Sand. A discrete gradation of substantially 2.38—0.225 mm (8—65 mesh) size provides a versatile fine aggregate or sand for road mixtures, concrete, plaster, or any constmcfion use suppHed by siHca sand. The only disadvantage is that in many areas conventional sand is less cosdy. 

Paper consists of sheet materials that are comprised of bonded small discrete fibers. The fibers usually are ceUulosic in nature and are held together by hydrogen bonds (see Cellulose). The fibers are formed into a sheet on a fine screen from a dilute water suspension. The word paper is derived from papyms, a sheet made in ancient times by pressing together very thin strips of an Egyptian reed Cjperuspapyrus) (1). 

Numerical simulations offer several potential advantages over experimental methods for studying dynamic material behavior. For example, simulations allow nonintrusive investigation of material response at interior points of the sample. No gauges, wires, or other instrumentation are required to extract the information on the state of the material. The response at any of the discrete points in a numerical simulation can be monitored throughout the calculation simply by recording the material state at each time step of the calculation. Arbitrarily fine resolution in space and time is possible, limited only by the availability of computer memory and time. 

Bubble flow - The gas is roughly uniformly distributed in the form of small discrete bubbles in a continuous liquid phase. The flow pattern is designated as bubble flow (B) at low liquid flowrates, and as dispersed bubble (DB) at high liquid flow rates in which case the bubbles are finely dispersed in the liquid. 

For tasks that rely on decision-making rather than on fine manipulations, the activity chart can assume a columnar format, with columns recording process information attended and subsequent changes of discrete control settings. 

B. Fine and G. Rosenberger, Algebraic Generalizations of Discrete Groups (1999)... 

Large-scale numerical simulation for samples that are many times os large as the critical wavelength is perhaps the only way to develop a quantitative understanding of the dynamics of solidification systems. Even for shallow cells, such calculations will be costly, because of the fine discretizations needed to be sure the dynamics associated with the small capillary length scales are adequately approximated. Such calculations may be feasible with the next generation of supercomputers. 

Solids appear in one of two forms, either as crystals or powders. The difference is one of size, since many of the powders we use are in reality very fine crystals. This, of course, depends upon the manner in which the solid is prepared. Nevertheless, most solids that we encounter in the real world are in the form of powders. That is, they are in the form of discrete small particles of varying size. Each particle has its own unique diameter and size. Additionally, their physical proportions can vary in shape from spheres to needles. For a given powder, aU grains will be the same shape, but the particle shape and size can be eiltered by the method used to create them in the first place. Methods of particle formation include ... 

All of these variables must be optimized simultaneously to obtain the best design. Some of the variables are continuous and some are discrete (the number of stages in each column section). Such optimizations are far from straightforward if carried out using detailed simulation. It is therefore convenient to carry out some optimization using shortcut methods before proceeding to detailed simulation where the optimization can be fine-tuned. 

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