Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

On a perturbed anisotropic equation with a critical exponent

Abstract We study a perturbed anisotropic equation without using the knowledge of the limiting problem. This provides a different method from that introduced by Brézis and Nirenberg [4]. Our arguments use some tools recently developed in [5, 6]. Keywords: Anisotropic critical exponent, Critical level, Compactness, Nehari manifold Mathematics Subject Classification (2000): 35J25, 35J60, 35J65     

Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

Stationary axisymmetric solutions in the vacuum Jordan-Brans-Dicke theory

It is shown that any stationary axisymmetric solution to the vacuum field equations of the Jordan-Brans-Dicke (JBD) theory may be obtained from a composition of any stationary axisymmetric vacuum Einstein spacetime with the Weyl class of metrics. Thus, generating solution techniques can be used to obtain any stationary axisymmetric JBD vacuum solution. In this manner, C. B. G. McIntosh's results concerning this topic are improved upon.     

Existence et prolongement des solutions holomorphes des équations aux dérivées partielles

Sans résumé     

Nonlinear behaviour of the instability of steady natural convection in a vertical air layer

In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method.     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.     

Synthesis of 3-Adenyl- and 3-Thyminylcyclobutane-1,1-dimethanols and Their Homo-octameric Phosphodiesters

Starting from 3-(benzyloxy)cyclobutane-1,1-dimethanol, 3-thyminyl- and 3-adenylcyclobutane-1,1-dimethanol were synthesized by direct introduction of the heterocycles (Scheme 1). The mono-O-substituted methoxytrityl derivatives were separately converted to octameric phosphodiesters on an aminomethyl-polystyrene carrier by the phosphotriester method. These oligomers of carba-nucleosides were prepared in order to study their annealing behaviour towards ribo- and deoxyribo-nucleic acids as well as their potential for homologous hybridization.     

First-order distributed feedback dye laser effect in reflection pumping geometry

Tunable distributed feedback lasing output based on reflection grating configuration instead of the traditional transmission one was realized from rhodamine 6G (R6G)-doped ethanol and 4-dicyanomethylene-2-methyl-6- (p-dimethylaminostyryl)-4H-pyran-(DCM)-doped methanol. Pure gain coupling and additional index coupling were obtained in R6G-doped ethanol and DCM-doped methanol, respectively. The tuning, which was found to be independent of the refractive index of the lasing media, went through the entire stimulated emission band for the two cases. Dual-peak lasing emission indicative of the existence of an index grating was observed in DCM-doped methanol. The interval between the two peaks increased with pump energy.