It must be recognized that the symbols in the equations of this article represent the complex multipliers of e ^ { j \ omega t }, giving the in-phase and out-of-phase parts with respect to the chosen reference . The complex vector multipliers of e ^ { j \ omega t } may be called " vector phasors " by analogy to the complex scalar quantities which are commonly referred to as " phasors ".
32.
The reason is that 1 / | x | 2 is not a solution of any physically reasonable linear PDE in 2D or 3D . Said in another way, a superposition principle does hold for sound waves, what reflects their mathematical description as solution of the linear wave equation \ scriptstyle ( \ partial _ { tt }-\ Delta ) w = 0; but the sound intensity as a scalar quantity, seems related in a " nonlinear " way to the sound waves, so that the additivity should be destroyed.
33.
The external force K is multiplied by time ( " t " ), where " K " is a positive scalar constant, however this can be varying and or negative as well . " S " represents the state of a cell ( + 1 or " 1 ), the second component takes the sum of the four neighbouring cell states ( up, down, left & right ) and multiplies it by another scalar quantity, this is analogous to a coupling constant ( " J " ).
