2 5 Ju l 1 99 9 Waves on Icicle NAOHISA OGAWA

Surface instability of icicles.

Quantitatively unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1-mm-thick layers of water flow down an icicle. These waves typically have a wavelength of about 1 cm, which is independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper, we show that these waves cannot be obtained by a naive Mullins-Seke...

ar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES

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ar X iv : n uc l - th / 9 90 60 29 v 3 1 5 Ju l 1 99 9 1 Quark Matter ’ 99 — Theoretical Summary : What Next ?

ar X iv : m at h / 99 07 18 5 v 1 [ m at h . M G ] 2 9 Ju l 1 99 9 Higher dimensional flexible polyhedra ∗

It is show that sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each n ≥ 3. 1991 Mathematics Subject Classification: 52C25, 52B11.

ar X iv : m at h / 99 07 08 5 v 1 [ m at h . G R ] 1 3 Ju l 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS