Computer terminology

This discussion applies to numerical values of variables whose possible range constitutes a continuum in computer terminology these are called real numbers, as opposed to integers. Integers should be identified as such, and all of the digits necessary to express them should be given. 

In computer terminology, speed has two chief varieties clock speed and bandwidth. Clock speeds, which give an indication of how fast a processor runs, have units of Hertz (Hz), or cycles per second. In this case, standard prefix meanings are used, so one megaHertz is 10 cycles per second. The simplest computer instructions require one dock cycle to be executed, so a processor with a clock speed of one megaHertz would be able to execute one instruction in one microsecond, and a gigaHertz processor could execute one instruc-... 

No digital image is as good as the human eye s view of an actual object. The smaller the number of stored points of the image (known in computer terminology as pixels) the poorer is its quality. 

The largest computers now include disk storage space measured in terabytes. How many bytes are in a terabyte (Recall that in computer terminology, the prefix is only close to the value it designates in the metric system.)... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

This chapter is in no way meant to impart a thorough understanding of the theoretical principles on which computational techniques are based. There are many texts available on these subjects, a selection of which are listed in the bibliography. This book assumes that the reader is a chemist and has already taken introductory courses outlining these fundamental principles. This chapter presents the notation and terminology that will be used in the rest of the book. It will also serve as a reminder of a few key points of the theory upon which computation chemistry is based. 

Computational results can be related to thermodynamics. The result of computations might be internal energies, free energies, and so on, depending on the computation done. Likewise, it is possible to compute various contributions to the entropy. One frustration is that computational software does not always make it obvious which energy is being listed due to the dilferences in terminology between computational chemistry and thermodynamics. Some of these differences will be noted at the appropriate point in this book. 

There are many good books describing the fundamental theory on which computational chemistry is built. The description of that theory as given here in the first few chapters is very minimal. We have chosen to include just enough theory to explain the terminology used in later chapters. 

It covers the principles of engineering drawings, computer graphics, descriptive geometry, and problem solving. The overall study of graphics involves the three basic aspects of terminology, skills, and theory. 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

A method for smoothing the residual obtained on the fine grid in order to compute the corresponding residual on the coarse grid. In the terminology of the multigrid method, this step is called restriction. 

You may be surprised that for our example data from Miller and Miller ([2], p. 106), the correlation coefficient calculated using any of these methods of computation for the r-value is 0.99887956534852. When we evaluate the correlation computation we see that given a relatively equivalent prediction error represented as (X - X), J2 (X - X), or SEP, the standard deviation of the data set (X) determines the magnitude of the correlation coefficient. This is illustrated using Graphics 59-la and 59-lb. These graphics allow the correlation coefficient to be displayed for any specified Standard error of prediction, also occasionally denoted as the standard error of estimate (SEE). It should be obvious that for any statistical study one must compare the actual computational recipes used to make a calculation, rather than to rely on the more or less non-standard terminology and assume that the computations are what one expected. 

The prior distribution is often not what is observed, and there can be extreme deviations from it. [1, 3, 23] By our terminology this means that the dynamics do impose constraints on what can happen. How can one explicitly impose such constraints without a full dynamical computation At this point I appeal again to the reproducibility of the results of interest as ensured by the Monte Carlo theorem. The very reproducibility implies that much of the computed detail is not relevant to the results of interest. What one therefore seeks is the crudest possible division into cells in phase space that is consistent with the given values of the constraints. This distribution is known as one of maximal entropy". 

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