Basic Theories and Concepts

Mathematically, studies of diffusion often require solving a diffusion equation, which is a partial differential equation. The book of Crank (1975), The Mathematics of Diffusion, provides solutions to various diffusion problems. The book of Carslaw and Jaeger (1959), Conduction of Heat in Solids, provides solutions to various heat conduction problems. Because the heat conduction equation and the diffusion equation are mathematically identical, solutions to heat conduction problems can be adapted for diffusion problems. For even more complicated problems, including many geological problems, numerical solution using a computer is the only or best approach. The solutions are important and some will be discussed in detail, but the emphasis will be placed on the concepts, on how to transform a geological problem into a mathematical problem, how to study diffusion by experiments, and how to interpret experimental data. 

In addition to the similarity between the heat conduction equation and the diffusion equation, erosion is often described by an equation similar to the diffusion equation (Culling, 1960 Roering et al., 1999 Zhang, 2005a). Flow in a porous medium (Darcy s law) often leads to an equation (Turcotte and Schubert, 1982) similar to the diffusion equation with a concentration-dependent diffu-sivity. Hence, these problems can be treated similarly as mass transfer problems. 

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The scope of this book is to outline the basic theories and concepts that may be encountered by a researcher in the course of basic electrochanical experimentation. This section... 

H. Nakamura, Nonadiabatic Transition Concepts, Basic Theories and Applications, World Scientific, Singapore, 2002. 

While not denying that theories and concepts derived in basic scientific research can lead to new types of technology,6 there is another important way in which science can be applied to technology through technology (rather than nature) as the object of science. In this spirit the Royal Society was established to... 

Many pilot studies and field cases have been summarized an effort has been made to select these studies and cases so that each one addresses unique issues. This book also proposes some new concepts and ideas or hypotheses. Several of them need to be validated by further research, and some may stimulate other research interests. From this standpoint, this book could be useful to researchers. The basic theories and sample calculations should help students and professionals who are less experienced in this area. This book also may be used by environmental engineering professionals who work on cleaning up wastes and nonaqueous phase liquids (NAPE). In addition, an effort has been made to strike an ideal balance between theory and practice in addition, extensive references are provided. 

The objective of this chapter is to provide the reader with a concise overview of HPLC terminology and concepts. Both basic and selected advanced concepts are covered. The reader is referred to other HPLC textbooks,1-7 training courses,8-9 journals, and Internet resources for a more detailed treatment of HPLC theory and concepts. This chapter has the following sections ... 

Unfortunately, there is no one ideal additive since each of the infinite number of end uses will call for a particular set of characteristic, including diverging properties. Recognize that, like a sea-saw, improvements in one property can lead to deterioration in others. In addition, the effectiveness of compounding additives depends also on the correct procedure of incorporation into the plastic matrix. The compatibility and diffusibility of additives is normally assessed fi-om experience or by trial and error. The basic theories and knowledge of solution thermodynamics may be used to determine potential compatibility. The theories of their behaviors do exist so that they can be used in the preliminary concepts to meet specific performances. 

The concept of the phantom network is completely defined by Eqs. (6)- 8). Its treatment is outlined in Sect. 3. It is worth noting that non-reduced connectivity matrices, describing both the connection of the segments in the linear parts of the network and the connection of the chains by the crosslinks, are a suitable basis for a theory of the dynamical properties of the phantom network. The basic theory and applications can be found in Refs. 

Literature has many theories and concepts discussing human reliability and associated human error causal factors that always trigger incidents and accidents within safety-critical systems. The main - by definition - characteristics of such safety occurrences are their randonmess, rare predictability, sophisticated, yet vague sequence of propagation. Such characteristics can basically allow for the retrospective analysis of these occurrences and their causes at various sectors and levels within industry such that re-occurrence margins are reduced if not totally eliminated. The major drawback of such reactive treatment... 

Because the modern, quantitative approach to interface and colloid science is a relatively new development, a great deal remains to be done in terms of extending the basic ideas and concepts originating in the classic period of the science to include new information and theories. Not only the desire for improved theories, but technological innovation demands that our understand-... 

Part II reviews some of the basic theories and principles in the design of SHE information systems. Thereafter, an accident model is introdnced that represents a synthesis of many existing models. It provides a framework for a presentation of the different types of methods and tools in Parts HI to V. Part II also introduces a number of theoretical concepts and principles including accident-barrier theory, theories on human performance and errors, and feedback mechanisms in decision-making. This part ends with a set of criteria for the evaluation of SHE information systems. 

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