Computational basic aspects

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. 

R.Carbo and B.Calabuig, "A project for the development of a computational system, based on PC-compatible computers to be used in Quantum Chemistry teaching and research", pp. 73-90 in R.Carbo (Editor), Quantum Chemistry, Basic Aspects. Actual Trends. Studies in Physical and Theoretical Chemistry. Vol. 62, Elsevier, Amsterdam, 1989. 

Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

Before discussing some applications, a few basic aspects on univariate statistics will be presented. A large amount of information exists regarding this field, and more details can be found in the original literature (e.g. [70,71]). Also a variety of computer packages performing statistical data analysis is available (e.g. [71a]). 

Computer simulations, Monte Carlo or molecular dynamics, in fact appear to be the actual most effective way of introducing statistical averages (if one decides not to pass to continuous distributions), in spite of their computational cost. Some concepts, such as the quasi-structure model introduced by Yomosa (1978), have not evolved into algorithms of practical use. The numerous versions of methods based on virial expansion, on integral equation description of correlation functions, on the application of perturbation theory to simple reference systems (the basic aspects of these... 

Although considerable advances have been made both in understanding the basic aspects of slurry bubble column reactors (SBCR) and in developing rational design procedures, computational fluid dynamics (CFD) - assisted design methodology for reactor optimization is sparse. 

The actual discussion has the aim to adopt this previous spirit, but obviously choosing a much more modest point of view, attached to Quantum Similarity Measures (QSM). This work is focused to explore the various possible extensions for the study of DF, the auxiliary building block elements of QSM [16-38]. In order to fulfil such a purpose, this study will start analysing a sound formal basis as a first step to understand the role of momentum operators in computational Quantum Chemistry. From this introductory position, it will be finally obtained a general pattern enveloping the whole area of DF study, beginning at the basic aspects and ending over the final applications of extended DF definitions. 

This chapter focuses on virtual reality (VR) applications in the fields of engineering and industrial engineering. It gives definitions of the main keywords for the field of engineering and describes the hardware and software and the specific human-computer interaction aspects for virtual environments (VE). Some typical applications are specified that show the field-tested use of VR, and the basics for the integration of such applications in the development process are described. 

To provide a basis for both the theoretical ideas and the computational techniques that we will discuss in this chapter, we start by reminding the reader of some essential concepts. Section 2.1 reviews some basic aspects of the Helfrich Hamiltonian. Section 2.2 introduces three coarse-grained membrane models that will be used in the remainder of this chapter. In Sects. 2.3 and 2.4, we discuss the bending moduli and the surface tension of membranes in more detail, and finally comment on multicomponent membranes in Sect. 2.5. 

As anticipated in the introduction, since most of the UV-vis spectra are recorded in the condensed phase, suitable theoretical models, able to include the effect of the solvent on the absorption and the emission spectra, are necessary. This topic has been discussed in detail in several reviews, and thus, also in this case, we limit our discussion to some basic aspects [41, 78]. The most direct procedure to compute the spectra of a given molecule (the solute) in solution consists in including in the calculations a certain number of explicit solvent molecules [79, 80]. However, this approach has to face two severe difficulties (i) the number of solvent molecules necessary to reproduce the bulk properties of a liquid (say, its macroscopic dielectric constant) is very large (ii) a dynamical treatment averaging all the possible configurations of the solvent molecules is in principle necessary. As a consequence, this approach has a large computational cost, especially when used for studying... 

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

Recent years have witnessed an increase in the number of people using computational chemistry. Many of these newcomers are part-time theoreticians who work on other aspects of chemistry the rest of the time. This increase has been facilitated by the development of computer software that is increasingly easy to use. It is now so easy to do computational chemistry that calculations can be performed with no knowledge of the underlying principles. As a result, many people do not understand even the most basic concepts involved in a calculation. Their work, as a result, is largely unfocused and often third-rate. 

The transputer s advantage in speed relative to common computer operations has also been boosted by reducing the number of basic instruction sets available to the programmer. This aspect is discussed next. 

Dente and Ranzi (in Albright et al., eds.. Pyrolysis Theory and Industrial Practice, Academic Press, 1983, pp. 133-175) Mathematical modehng of hydrocarbon pyrolysis reactions Shah and Sharma (in Carberry and Varma, eds.. Chemical Reaction and Reaction Engineering Handbook, Dekker, 1987, pp. 713-721) Hydroxylamine phosphate manufacture in a slurry reactor Some aspects of a kinetic model of methanol synthesis are described in the first example, which is followed by a second example that describes coping with the multiphcity of reactants and reactions of some petroleum conversion processes. Then two somewhat simph-fied industrial examples are worked out in detail mild thermal cracking and production of styrene. Even these calculations are impractical without a computer. The basic data and mathematics and some of the results are presented. 

In an outreach to the medicinal chemists at Lilly, a one-week workshop was created and taught in the research building where the organic chemists were located. (The computational chemists were initially assigned office space with the analytical chemists and later with the biologists.) The workshop covered the basic and practical aspects of performing calculations on... 

Airlift loop reactor (ALR), basically a specially structured bubble column, has been widely used in chemical industry, biotechnology and environmental protection, due to its high efficiency in mixing, mass transfer, heat transfer etc [1]. In these processes, multiple reactions are commonly involved, in addition to their complicated aspects of mixing, mass transfer, and heat transfer. The interaction of all these obviously affects selectivity of the desired products [2]. It is, therefore, essential to develop efficient computational flow models to reveal more about such a complicated process and to facilitate design and scale up tasks of the reactor. However, in the past decades, most involved studies were usually carried out in air-water system and the assumed reactor constructions were oversimplified which kept itself far away from the real industrial conditions [3] [4]. 

Another aspect of quantum chemical activity which we connect with group 1 is the formal elaboration of new approaches. At the beginning of the "computational era" (i.e. 30 years ago) there has been a blossoming of new formulations and new approaches which have given origin to to computer algorithms constituting the basic structure of today in-depth... 

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