Suffix notation

Via this Reynolds decomposition and after subsequent averaging all terms of the NS equations, the so-called turbulent or Reynolds stresses upf emerge in the transport equations, where these stresses represent the additional averaged momentum transport due to the eddies. These stresses may be resolved explicitly from separate transport equations which in suffix notation (usual in the field of turbulence) look as follows ... 

The repeated suffix notation is still being used but now the subscripts take numbers 1 through 6. The components, c.j, are called the elastic stiffness constants and they also form a symmetric array, reducing the required number of elastic constants to 21. As these constants are properties of a material, the sym-... 

Suffix notation 1st suffix - direction of normal to area. 2nd suffix - direction in which component acts. 

A corresponding change in the suffix notation for the stress components follows the same scheme as in Eq. (5.8.13). We thus specify the first component of the polarization vector as... 

The direction of a normal stress relative to Cartesian axes is denoted by a suffix notation is the normal stress component... 

To denote the directions of shear stresses a two-suffix notation is needed. In the usual convention the first suffix denotes the direction of the normal to the plane in which the stress acts and the second gives the direction of the shear stress component. For... 

When the strains are small (infinitesimal strains in the limiting case of the strain approaching zero) more precise definitions of the strain can be given. A suffix notation can also conveniently be introduced. Consider a section of a body in the xy plane, as in Fig. 2.4. Set up perpendicular lines in space to be the x and y... 

Hint Use the two-suffix notation and the relations between the elastic constants for cubic crystals discussed in Sect.3.6. 

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]. 

Using this notation the introduction of o into the suffix indicates an overall transfer unit. 

Before proposing a general formulation, we illustrate a DIFF with a simple case, in which we consider bone collagen as the body component, and the diet as containingjust two components, protein and non-protein. In the notation, B stands for body 5 values, and D for diet 8 values suffixes distinguish the particular component specified. Thus Bcolla stands for the collagen 8 C, Dp and Dn for the dietary protein and non-protein 6 C values. 

The nomenclature usually assumes R = Me, and substitution of methyl groups is indicated by a superscript suffix, e.g. Dph represents the unit Me(Ph)SiO(o.5)2, or with the substituted group following a prime notation and enclosed in brackets, e.g. M(D A)M. 

Many transition metals and the group of six elements centered around lead on the periodic table commonly have more than one valence. The valence of these metals in a compound must be known before the compound can be named. Modern nomenclature rules indicate the valence of one of these metals with a Roman numeral suffix (Stock notation). Older nomenclature rules used different suffixes to indicate the charge. Examples ... 

The Roman numeral suffix is part of the name of the metal. Thus iron(III) is one word. Stock notation should be used for all metals that have a variable valence. This includes almost all the transition elements and the elements immediately around lead on the periodic table. Stock notation is often omitted for Zn, Cd, and Ag, as they do not have variable valence. The valences of some common metals and acids are listed in Appendix C. 

In tensor notation the three Cartesian directions x, y, and z are designated by suffixed variables i,j, k, l, etc. (Landau and Lifshitz 1970 Auld 1973). Thus the force acting per unit area on a surface may be described as a traction vector with components rj j = x, y, z. The stress in an infinitesimal cube volume element may then be described by the tractions on three of the faces, giving nine elements of stress cry (i, j = x, y, z), where the first suffix denotes the normal to the plane on which a given traction operates, and the second suffix denotes the direction of a traction component. 

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

The following notation is introduced and unless otherwise stated the suffixes 1 and 2 refer to quantities in the gas and liquid phases respectively ... 

These equations use Cartesian tensor notation in which a repeated Greek suffix denotes summation over the three components, and where ay7 is the third-rank antisymmetric unit tensor. For a molecule composed entirely of idealized axially symmetric bonds, for which [3 (G )2 = /3(A)2 and aG1 = 0 [13, 15], a simple bond polarizability theory shows that ROA is generated exclusively by anisotropic scattering, and the CID expressions then reduce to [13]... 

Even though we do not invoke the full machinery of tensor analysis (Butkov, 1968), it is useful to keep the distinction between contravariant and covariant components clear. To avoid conflicting notation we do not use upper and lower indices to denote contravariant and covariant indices. Instead, we will use the suffix ao (lower case letters) on tensors whose indices are all contravariant, and AO (capital letters) on tensors whose indices are all covariant. No special suffix is used in the MO basis. For example, using the two- and four-index trace operators the energy is... 

The notation of this chapter is quite parochial in its ambit and each symbol should be identifiable in its own context. In general, lower case letters have been used to designate the concentrations of the species denoted by the corresponding capitals, except that, as usual, c denotes the concentration of A J, Lower case s with various affixes are used for rate constants and the suffixed capitals of this letter represent equilibrium constants. Time is denoted by t and dimensionless time by t. 

If is not a function of direction, the intensity field is said to be isotropic. If /jt is not a function of position the Held is said to be homogeneous. The total intensity of radiation is / = /i dk. In the rest of this chapter, we suppres.s the suffix k to simplify the notation. 

The nomenclature of FA reflects the long history of their smdy and description. Most FA were originally described under trivial names prior to the adoption of the international molecular nomenclature rules in 1892 (Table 3.1). Even after adopting the International Union of Pure and Applied Chemistry (lUPAC) system for nomenclature (lUPAC-IUB, 1977), the habit of assigning trivial names to FA continues. The basis of the systematic nomenclature system is an extension of that accepted for hydrocarbon (alkane/alkene) naming. Hence, the descriptive name is based on the number of carbon atoms contained in the molecule, with the suffix -e replaced with -oic acid. However, in most instances, FA are referred to by their formula notations. As is the case with systematic and trivial names, there exists an lUPAC accepted formula notation nomenclature and several earher versions (Table 3.2). Each system... 

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