Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two‐state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch–bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two‐state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method

The highly excited C-H stretching states of CHD_3, CHT_3, and CH_3D

Unlike many other molecules having local modes, the highly excited C-H stretching states of CHD_3 show well resolved experimental spectra and simple Fermi resonance behavior. In this paper the local mode features in this prototype molecule are examined using a curvilinear coordinate approach. Theory and experiment are used to identify the vibrational state coupling. Both kinetic and potential terms are employed in order to characterize the coupling of the C-H stretch to various other vibrational modes, notably those including D-C-H bending. Predictions are also made for CHT_3 and the role of dynamical coupling on the vibrational states of CH_3D explored. Implications of these findings for mode-specific and other couplings are discussed

Origin and reduction of wakefields in photonic crystal accelerator cavities

Photonic crystal (PhC) defect cavities that support an accelerating mode tend to trap unwanted higher-order modes (HOMs) corresponding to zero-group-velocity PhC lattice modes at the top of the bandgap. The effect is explained quite generally from photonic band and perturbation theoretical arguments. Transverse wakefields resulting from this effect are observed in a hybrid dielectric PhC accelerating cavity based on a triangular lattice of sapphire rods. These wakefields are, on average, an order of magnitude higher than those in the waveguide-damped Compact Linear Collider (CLIC) copper cavities. The avoidance of translational symmetry (and, thus, the bandgap concept) can dramatically improve HOM damping in PhC-based structures.Comment: 11 pages, 18 figures, 2 table

Inflating magnetically charged braneworlds

Numerical solutions of Einstein, scalar, and gauge field equations are found for static and inflating defects in a higher-dimensional spacetime. The defects have $(3+1)$-dimensional core and magnetic monopole configuration in $n=3$ extra dimensions. For symmetry-breaking scale $\eta$ below the critical value $\eta_c$, the defects are characterized by a flat worldsheet geometry and asymptotically flat extra dimensions. The critical scale $\eta_c$ is comparable to the higher-dimensional Planck scale and has some dependence on the gauge and scalar couplings. For $\eta=\eta_c$, the extra dimensions degenerate into a `cigar', and for $\eta>\eta_c$ all static solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. The inflating solutions have de Sitter worldsheets and cigar geometry in the extra dimensions. Exact analytic solutions describing the asymptotic behavior of these inflating monopoles are found and the parameter space of these solutions is analyzed.Comment: 35 pages, revtex, 18 eps figure

MOVING FROM UNIFORM TO VARIABLE FERTILIZER RATES ON IOWA CORN: EFFECTS ON RATES AND RETURNS

This study develops a model based on the yield potential of various soil types in 12 Iowa counties to estimate the potential value of switching from uniform to variable fertilizer rates. Results indicate modest increases in the gross returns over fertilizer costs, ranging from $7.43 to$1.52 per acre. The net profitability of variable-rate technology (VRT) is sensitive to the per acre costs of moving to a VRT program. Under the assumptions of the model, applying variable rates would increase yield by 0.05 to 0.5 bushels per acre, and would reduce fertilizer costs by $1.19 to$6.83 per acre.Crop Production/Industries,

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics