Speed of the method

The speed of the method comes from two sources. First, all of the macroscopic cells of the same size have exactly the same internal structure, as they are simply formed of tessellated copies of the original cell, thus each has exactly the same multipole expansion. We need compute a new multipole expansion only once for each level of macroscopic agglomeration. Second, the structure of the periodic copies is fixed we can precompute a single transfer... 

Use of electron capture detectors increases the sensitivity to halothane and decreases the relative sensitivity to heptane, improving the overall sensitivity and speed of the method (64, 65). 

We have shown, in agreement with the results presented in Ref. 21, that the method of classical trajectories gives very good predictions in the case of strong-field interactions (i.e., for the photon numbers larger than 10). The calculation speed of the method does not depend on numbers of interacting... 

Another method for the determination of polymer crystallinity was discussed by Duswalt (159). It is based on the ability of the instrument to cool a molten sample rapidly and reproducibJy to a reselected temperature where isothermal crystallization is allowed to occur. A number of crystallization curves for polyethylene obtained isothermalJy at different, preset crystallization temperatures are shown in Figure 7.57. Differences in polymer crystallizability that may be caused by branching, nucleation, or molecular weight effects can be observed. The sensitivity and speed of the method allow pellet-to-pellet variations in a lot of polymer to be examined. 

The high sensitivity, resolving power, ease, and speed of the method make this an excellent means of critical assessment of purity of amino acid derivatives [88,89]. Typically, elution of derivatives is from a small-diameter (5-10 m, 300 A pore size) reversed phase (RP) support using a linear gradient of acetonitrile in aqueous buffer. Gradients are usually from 30% B to 100% B over 30 min. The following buffer systems are widely used, and it is recommended that at least one be employed for the determination of derivative purity. 

These methods essentially follow the rote procedure outlined above. The important difference is that the mass action, mass balance, and charge balance equations are written in generalized mathematical notation. They can then be applied to any chemical system by specifying the reactions and species of interest. The approach we outline here is described in detail by Crerar (1975). However, we include a change in the mass action equations which was not in the original paper this improves the speed of the method and its chances of success with very complex systems. Consider an bitrary system of c components containing N chemical species. Equilibrium constants are known for M independent reactions relating some or all of these species. 

Suppose we are interested in calculating all EFMs with a maximal cardinality of their support. In this case, we can omit an intermediate extreme ray from the analysis as soon as the number of positive entries in the first p -T k components exceeds the maximal cardinality. By omitting intermediate extreme rays, the combinatorial explosion of extreme rays is curbed and the method becomes applicable to larger networks, without compromising the efficiency and speed of the method. 

The extraction of knowledge from spectroscopic data is of great interest since spectroscopic methods play a major role in structure identification and elucidation as well as in quantitative analysis. IR spectroscopy is a very useful method because of the high information content of an IR spectrum and its broad applicability. This is due to the speed of the method, both for the analysis itself and the time window that can be observed, and the simple techniques for sample preparation. 

The usefulness of semiempirical methods is determined by four quantities the speed of the method, the accuracy and the generality of the method, and the ease of use. Parameterization is one stage in the development of a new method, and the accuracy of the method is determined to a large degree by how well the values of the parameters are determined. The other three considerations are not affected in any way by parameterization. 

The procedure is computationally efficient. For example, for the catalytic subunit of the mammalian cAMP-dependent protein kinase and its inhibitor, with 370 residues and 131 titratable groups, an entire calculation requires 10 hours on an SGI 02 workstation with a 175 MHz MIPS RIOOOO processor. The bulk of the computer time is spent on the FDPB calculations. The speed of the procedure is important, because it makes it possible to collect results on many systems and with many different sets of parameters in a reasonable amount of time. Thus, improvements to the method can be made based on a broad sampling of systems. 

Most of the problems in this book are simple. Many of the methods used have been known for decades or for centuries. At the machine level, individual steps in the procedures are at the grade school level of sophistication, like adding two numbers or comparing two numbers to see which is larger. What makes them hard is that there are very many steps, perhaps many millions. The computer, even the once lowly microcomputer, provides an entry into a new scientific world because of its incredible speed. We are now in the enviable position of being able to arrive at practical solutions to problems that we could once only imagine. 

Since viscometer drainage times are typically on the order of a few hundred seconds, intrinsic viscosity experiments provide a rapid method for evaluating the molecular weight of a polymer. A limitation of the method is that the Mark-Houwink coefficients must be established for the particular system under consideration by calibration with samples of known molecular weight. The speed with which intrinsic viscosity determinations can be made offsets the need for prior calibration, especially when a particular polymer is going to be characterized routinely by this method. 

Pulpstones. Improvements have been made in the composition and speed of the grinding wheel, in methods of feeding the wood and pressing it against the stone, in control of power to the stones, and in the size and capacity of the units. The first pulpstones were manufactured from quarried sandstone, but have been replaced by carbide and alumina embedded in a softer ceramic matrix, in which the harder grit particles project from the surface of the wheel (see Abrasives). The abrasive segments ate made up of three basic manufactured abrasive siUcon carbide, aluminum oxide, or a modified aluminum oxide. Synthetic stones have the mechanical strength to operate at peripheral surface speeds of about 1200—1400 m /min (3900 to 4600 ft/min) under conditions that consume 0.37—3.7 MJ/s (500—5000 hp) pet stone. 

The most successful models are based on the finite element method. The flow is discretized into small subregions (elements) and mass and force balances are appHed in each. The result is a large system of equations, the solution of which usually gives the speed of the coating Hquid in each element, pressure, and the location of the unknown free surfaces. The smaller the elements, the more the equations which are often in the range of 10,000 to upward of 100,000. 

Such a control is good for machines that are required to operate at low speeds with a high accuracy. Now the phasor /, in terms of /, , is varied according to the speed required. Figure 6.2 now changes to Figure 6.8, which is a marked improvement on the earlier characteristics. The torque variation with speed is now almost constant, except at very low speeds. The reason for poor torque at low speeds is the method of speed variation which is. still based on Vlf. Now a motor s mathematical model is used... 

To approximate the rotational speed of the belt, the linear speed may be calculated using the pitch diameters and the center-to-center distance (see Figure 44.5) between the sheaves. This method is accurate only if there is no belt sag. Otherwise, the belt rotational speed obtained using this method is slightly higher than the actual value. 

A similar method of test was used at the International Nickel Company s Corrosion Laboratory at North Carolina. The specimen discs are mounted on insulated vertical spindles and submerged in sea-water, which is supplied continuously to the tank in which the specimens are immersed. The maximum peripheral speed of the spinning disc is about 760cms , and the characteristic pattern of attack is shown in Fig. 19.3a. Studies of variation of depth of attack with velocity indicate that at low velocities (up to about 450 cm s ) alloys such as Admiralty brass, Cu-lONi and cupro-nickel alloys containing iron maintain their protective film with a consequent small and similar depth of attack for the diflferent alloys. At higher velocities the rate increases due to breakdown of the film. 

Alternative procedure. The following method utilises a trace of copper sulphate as a catalyst to increase the speed of the reaction in consequence, a weaker acid (acetic acid) may be employed and the extent of atmospheric oxidation of hydriodic acid reduced. Place 25.0 mL of 0.017M potassium dichromate in a 250 mL conical flask, add 5.0 mL of glacial acetic acid, 5 mL of 0.001M copper sulphate, and wash the sides of the flask with distilled water. Add 30 mL of 10 per cent potassium iodide solution, and titrate the iodine as liberated with the approximately 0.1M thiosulphate solution, introducing a little starch indicator towards the end. The titration may be completed in 3-4 minutes after the addition of the potassium iodide solution. Subtract 0.05 mL to allow for the iodine liberated by the copper sulphate catalyst. 

---