Simulating the Physical World: Hierarchical Modeling from Quantum Mechanics to Fluid Dynamics

Symbols, Units and Constants

Symbols

The typographic conventions and special symbols used in this book are listed in Table 1; Latin and Greek symbols are listed in Tables 2, 3, and 4. Symbols that are listed as vectors (bold italic, e.g., r) may occur in their roman italic version ( r = r) signifying the norm (absolute value or magnitude) of the vector, or in their roman bold version ( r) signifying a one-column matrix of vector components. The reader should be aware that occasionally the same symbol has a different meaning when used in a different context. Symbols that represent general quantities as a, unknowns as x, functions as f( x), or numbers as i, j, n are not listed.

Table 1: Typographic conventions and special symbols

Element

Example

Meaning

*

c*

complex conjugate c* = a ? bi if c = a + bi

? G

transition state label

hat

?

operator

overline

u

(1) quantity per unit mass, (2) time average

dot

time derivative

average over ensemble

bold italic (l.c.)

r

vector

bold italic (u.c.)

Q

tensor of rank ? 2

bold roman (l.c.)

r

one-column matrix,

e.g., representing vector components

bold roman (u.c.)

Q

matrix, e.g., representing tensor components

overline

u

quantity per unit mass

overline

M

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