Wave shoaling and the angular frequency is proportional to its local rate of change, Simplifying to one dimension and cross-differentiating it is now easily seen that the above definitions indicate simply that the rate of change of wavenumber is balanced by the convergence of the frequency along a ray; Assuming stationary conditions (formula_27), this implies that wave crests are conserved and the frequency must remain constant along a wave ray as formula_28. As waves enter shallower waters, the decrease in group velocity caused by the reduction in water depth leads to a reduction in wave length formula_29 because the nondispersive shallow water
Madelung constant Madelung constant allows for the calculation of the electric potential "V" of all ions of the lattice felt by the ion at position "r" where "r" =|"r" - "r"| is the distance between the "i"th and the "j"th ion. In addition, If the distances "r" are normalized to the nearest neighbor distance "r" the potential may be written with formula_3 being the (dimensionless) Madelung constant of the "i"th ion The electrostatic energy of the ion at site formula_5 then is the product of its charge with the potential acting at its site There occur as many Madelung constants formula_3 in