Trions in a periodic potential

The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations.Comment: revtex, 5 p., sub. to Physica

Drag and inertia coefficients for horizontally submerged rectangular cylinders in waves and currents

The results of an experimental investigation carried out to measure combined wave and current loads on horizontally submerged square and rectangular cylinders are reported in this paper. The wave and current induced forces on a section of the cylinders with breadth-depth (aspect) ratios equal to 1, 0.5, and 0.75 are measured in a wave tank. The maximum value of Keulegan-Carpenter (KC) number obtained in waves alone is about 5 and Reynolds (Re) number ranged from 6.3976103 to 1.186105. The drag (CD) and inertia (CM) coefficients for each cylinder are evaluated using measured sectional wave forces and particle kinematics calculated from linear wave theory. The values of CD and CM obtained for waves alone have already been reported (Venugopal, V., Varyani, K. S., and Barltrop, N. D. P. Wave force coefficients for horizontally submerged rectangular cylinders. Ocean Engineering, 2006, 33, 11-12, 1669-1704) and the coefficients derived in combined waves and currents are presented here. The results indicate that both drag and inertia coefficients are strongly affected by the presenceof the current and show different trends for different cylinders. The values of the vertical component inertia coefficients (CMY) in waves and currents are generally smaller than the inertia coefficients obtained in waves alone, irrespective of the current's magnitude and direction. The results also illustrate the effect of a cylinder's aspect ratio on force coefficients. This study will be useful in the design of offshore structures whose columns and caissons are rectangular sections