Scarlet Lily

Flowers in wooden pot; Wooden border around titlehttps://scholarsjunction.msstate.edu/cht-sheet-music/11261/thumbnail.jp

Jolly Jingles Rag

One person playing the banjo, and other people dancing on different parts of the coverhttps://scholarsjunction.msstate.edu/cht-sheet-music/13782/thumbnail.jp

Loyal Knights : March

https://digitalcommons.library.umaine.edu/mmb-ps/2467/thumbnail.jp

Dreams At Sunset : Hesitation Waltz

https://digitalcommons.library.umaine.edu/mmb-ps/2609/thumbnail.jp

Sun-Flower : Three Step

https://digitalcommons.library.umaine.edu/mmb-ps/2598/thumbnail.jp

Commander-in-Chief : March Two-Step

https://digitalcommons.library.umaine.edu/mmb-ps/2675/thumbnail.jp

Heather Bells : Three Step

https://digitalcommons.library.umaine.edu/mmb-ps/1023/thumbnail.jp

Melting and Rippling Phenomenan in Two Dimensional Crystals with localized bonding

We calculate Root Mean Square (RMS) deviations from equilibrium for atoms in a two dimensional crystal with local (e.g. covalent) bonding between close neighbors. Large scale Monte Carlo calculations are in good agreement with analytical results obtained in the harmonic approximation. When motion is restricted to the plane, we find a slow (logarithmic) increase in fluctuations of the atoms about their equilibrium positions as the crystals are made larger and larger. We take into account fluctuations perpendicular to the lattice plane, manifest as undulating ripples, by examining dual layer systems with coupling between the layers to impart local rigidly (i.e. as in sheets of graphene made stiff by their finite thickness). Surprisingly, we find a rapid divergence with increasing system size in the vertical mean square deviations, independent of the strength of the interplanar coupling. We consider an attractive coupling to a flat substrate, finding that even a weak attraction significantly limits the amplitude and average wavelength of the ripples. We verify our results are generic by examining a variety of distinct geometries, obtaining the same phenomena in each case.Comment: 17 pages, 28 figure

Starland : Reverie-Serenade

https://digitalcommons.library.umaine.edu/mmb-ps/1037/thumbnail.jp

Triumphant America : March-Two Step

https://digitalcommons.library.umaine.edu/mmb-ps/2486/thumbnail.jp