NOTATIONS AND CONVENTIONS

The above comments represent only some particularly chosen topics and events in the mathematical development of the continuum theory for liquid crystals, focusing especially on nematic and smectic C materials. In a book of this scope it is inevitable that some major topics have not been included, such as soliton-like behaviour in nematics or the flexoelectric effect, and many important contributions to the field have been omitted for the sake of brevity. Nevertheless, readers should have no difficulty in accessing these topics in the current literature if they have been armed with the material presented in subsequent Chapters. Interested readers can find more extensive details on the development of liquid crystals in the historical review by Kelker [143] or the forthcoming volume in this book series by Sluckin. Dunmur and Stegemeyer [253]. 

It is assumed throughout that the reader has some familiarity with index notation (also called suffix notation in what is presented here) and the Einstein summation convention. Many suitable introductions are available such as those provided by, for example, the books of Aris [4], Leigh [161], Goodbody [115] or Spencer [256], or the introductory notes by Leslie [174]. 

The terms Ot, i = 1,2,3, axe called the components of a. The Einstein summation convention allows the sum appearing in (1.1) to be expressed in a more succinct way so that we may write 

Two useful quantities that are employed throughout this book are the Kronecker delta Sij and the alternator eijk, defined when i, j and k can each take any of the values 1, 2 or 3. The Kronecker delta and the alternator are defined by, respectively. 

It is a common convention to denote the partial derivative with respect to the variable by a comma followed by the variable. For instance, means the partial derivative of the quantity p with respect to the variable. Similarly, aij indicates the partial derivative of the component of the vector a with respect to the variable. 

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It is important to discuss cell notation and conventions. Instead of drawing a complete diagram to present electrochemical cells, it is convenient to specify a cell in line formula form or, as may be said, shorthand form. The Cu-Zn cell is thus presented as ... 

Crystallography is an advanced discipline [318], Modern crystallography has been developed since the discovery of X-ray diffraction in 1912 from the original basis laid down by classical crystallographers. One of the beauties of this modern discipline, while it can be somewhat mathematical, is the universal use of standardised notations and conventions, as developed through the International Union of Crystallography (IUCr). 

A lot of notation and conventions are taken from [BBM], which is our main reference. 

Sullivan JF (1994) Notations and Conventions in Molecular Spectroscopy, Draft, to be published Surewicz WK, Epand RM, Orlowski R, Mant.sch HH (1987) Biochim Biophys Acta 899 307 Surewicz WK, Mantsch HH, Stahl GL, Epand RM (1987) Proc Natl Acad Sci USA 84 7028 Surewicz WK, Moscarello MA, Mantsch HH (1987) Biochemistry 26 3881 Surewicz WK, Moscarello MA, Mantsch HH (1987) J Biol Chem 262 8598 Suschtschinskij MM (1974) Raman Spektren von Molekiilen und Kristallen. Akademie Verlag Berlin... 

We use bold-face italic symbols for vectors and bold-face Greek symbols for second-order tensors dot-product operations enclosed in () are scalars, those in [ ] are vectors, and those in are second-order tensors. The vector-tensor notation and conventions are identical with those used by Bird, Stewart, and Lightfoot (8) unless otherwise indicated. 

Software documentation should include at least a user s guide and a theoretical Handbook. The latter is very important since different approaches are in use in many analyses. Another problem is the lack of established universal notation and conventions. 

Order a, a, a. A, A, A, PL (scripts and other), b, b, — subscripts and superscripts not ordered. Greek separately. See also Other notation and conventions. 

In this section we first introduce the quanmm numbers, notations and conventions usually associated with the description of rotational bands. Then we look at transitions within rotational bands and classify rotational bands according to their K quantum number. We then mm our attention to the influence the... 

The aim of this book is to present a mathematical introduction to the static and dynamic continuum theory of liquid crystals. Before doing so, we outline some points on the discovery and basic description of liquid crystals in Sections 1.1 and 1.2. This is followed by a short summary of the development of the continuum theory of liquid crystals in Section 1.3. The Chapter closes in Section 1.4 with some basic comments on the notation and conventions employed in later Chapters and refers to some sources for those who may require further background on some of these conventions used throughout this book. 

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