Resonant-frequency primitive waveforms and star waves in lattices

摘要: For square and triangular lattices we have found a new line-localized primitive waveform (LPW) existing at resonant frequency. In two-dimensional (2D) case, the LPW represents line of oscillating particles, while lattice outside this remains rest. We show that: (a) A single does not conduct energy; however, band consisting two or more neighboring LPWs is conductor with phase-shift-dependent energy flux velocity. (b) Any canonical sinusoidal wave consists LPWs. turn, can be represented by superposition waves (these types are connected discrete Fourier transform). (c) There (three) orientations for (triangular) lattice, why sinusoidal-wave group velocity orientation piecewise constant frequency; it coincides nearest orientation. (d) also exist lower frequency being localized halfplane boundary. Further, 3D plane-localized waveforms to in region. Finally, point harmonic excitation 2D that starlike develop rays directions.