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Using a lattice string model, a number of peculiar excitation situationsrelated to non-propagating excitations and non-radiating sources aredemonstrated. External fields can be used to trap excitations locally but alsolead to the ability to steer such excitations dynamically as long as thesteering is slower than the field's wave propagation. I present explicitconstructions of a number of examples, including temporally limitednon-propagating excitations, directional excitation and virtually slowedpropagation. Using these dynamical lattice constructions I demonstrate thatneither persistent temporal oscillation nor static localization are necessaryfor non-propagating excitations to occur.Comment: 16 pages, 5 figures, RevTex4, references added, figure captions  improved, to appear in Physical Review

Trapping and steering on lattice strings: Virtual slow waves and directional and nonpropagating excitations