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

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.
| 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 |