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In this note, we present a broad class of quarter-BPS solutions to matrixtheory, corresponding to non-commutative cylinders of arbitrary cross-sectionalprofile in R^8. The solutions provide a microscopic description of a generalsupertube configuration. Taking advantage of an analogy between a compactmatrix dimension and the Hamiltonian of a 1-dimensional crystal, we use a Blochwave basis to diagonalize the transverse matrices, finding a distribution ofeigenvalues which smoothly trace the profile curve as the Bloch wave number isvaried.Comment: 11 pages; v2 references added, introduction modified; v3 reference  adde

Bloch waves and fuzzy cylinders: 1/4-BPS solutions of matrix theory