Bloch wave – MoM method the wave numbers in any of the 3 periodic coordinate directions. This can happen for example when the free space wavelength exactly equals the lattice spacing. This is a statistically rare occurrence in computational practice and corresponds to a propagation anomaly similar to a Wood's reflection anomaly for gratings. To compute bands of the crystal (i.e. "k"-"k" diagrams), successive values of frequency ("k") are tried - in conjunction with pre-selected values of propagation constant ("k") and propagation direction (θ & φ) - until a combination is found which drives the determinant of the matrix to zero. Equation (4.2) has been
Champernowne constant Champernowne constant In mathematics, the Champernowne constant is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933. For base 10, the number is defined by concatenating representations of successive integers: Champernowne constants can also be constructed in other bases, similarly, for example: The Champernowne constants can be expressed exactly as infinite series: where formula_2 ceiling(formula_3), formula_4 in base 10, formula_5 and formula_6 is the base of the constant. A slightly different expression is given by Eric W. Weisstein (MathWorld): where formula_8