Flow in heated straight rotating pipe

Fully developed laminar flow in a straight heated rotating pipe which includes the influence of both, coriolis force and buoyancy force, has been considered analytically. The solution has been obtained in terms of series expansions; the solution is therefore restricted to small values of the parameters involved.     

Centrifugal (centripetal) and Coriolis' velocities and accelerations in $$ (\bar L_n,g) $$ -spaces

The notions of centrifugal (centripetal) and Coriolis' velocities and accelerations are introduced and considered in spaces with affine connections and metrics [ -spaces] as velocities and accelerations of flows of mass elements (particles) moving in space-time. It is shown that these types of velocities and accelerations are generated by the relative motions between the mass elements. They are closely related to the kinematic characteristics of the relative velocity and relative acceleration. The centrifugal (centripetal) velocity is found to be in connection with the Hubble law. The centrifugal (centripetal) acceleration could be interpreted as gravitational acceleration as has been done in the Einstein theory of gravitation. This fact could be used as a basis for workingout new gravitational theories in spaces with affine connections and metrics.     

High resolution infrared synchrotron study of CH2D81Br: ground state constants and analysis of the ν5, ν6 and ν9 fundamentals

The high resolution infrared absorption spectrum of CH₂D⁸¹Br has been recorded by Fourier transform spectroscopy in the range 550–1075?cm^?1, with an unapodized resolution of 0.0025?cm^?1, employing a synchrotron radiation source. This spectral region is characterized by the ν₆ (593.872?cm^?1), ν₅ (768.710?cm^?1) and ν₉ (930.295?cm^?1) fundamental bands. The ground state constants up to sextic centrifugal distortion terms have been obtained for the first time by ground-state combination differences from the three bands and subsequently employed for the evaluation of the excited state parameters. Watson's A-reduced Hamiltonian in the I^r representation has been used in the calculations. The ν ₆?=?1 level is essentially free from perturbation whereas the ν ₅?=?1 and ν ₉?=?1 states are mutually interacting through a-type Coriolis coupling. Accurate spectroscopic parameters of the three excited vibrational states and a high-order coupling constant which takes into account the interaction between ν₅ and ν₉ have been determined.     

The ν7, ν8, and ν11 bands of propynal, C2HCHO, in the 650 cm region

The infrared spectrum of propynal, C₂HCHO, is studied at high resolution (0.003 cm⁻¹) in the range 570-640 cm⁻¹. The relatively intense ν₁₁ (CC-H out-of-plane bend, 693 cm⁻¹) and ν₇ (CC-H in-plane bend, 651 cm⁻¹) fundamental bands are linked by a strong a-type Coriolis interaction. The somewhat weaker ν₈ (CCO in-plane bend, 614 cm⁻¹) fundamental has a significant Fermi-type interaction with the “dark” background state 3ν₉ (∼618 cm⁻¹). About 1400 lines are assigned and analyzed in terms of a four-state fit in order to obtain accurate band origins, rotational and centrifugal distortion parameters, and Fermi and Coriolis interaction parameters. This represents the first systematic high-resolution infrared study of propynal.     

Rotational analysis of the v7,v11 (a′,a″) pair of bands of the infrared spectrum of the deuterium substituted propynal molecule C2H-CDO

The mid-infrared spectrum of the v₇,v₁₁ (a′,a″) pair of bands of the deuterium substituted propynal molecule C₂H-CDO was recorded at a resolution of about 0.08 cm⁻¹. An analysis of the pair of bands was completed using the method of simulation of the observed bands with synthetic spectra taking into account the effects of second order Coriolis interactions between the energy levels of the two bands. Best fit values for the changes in the rotational constants (A″ − A′), (B″ − B′) and (C″ − C′), the second order Coriolis constant ζ_7,11 and the δ_7,11 = v₁₁ − v₇ constant have been derived.     

Diode laser absorption spectrum of cold bands of C2HD at 6500 cm

The absorption spectrum of acetylene-d has been observed at high resolution between 6470 and 6630 cm⁻¹ using an external cavity diode laser. Three cold bands have been observed: the strong 2ν₁ band, the weaker ν₁ + ν₂ + 2ν₅ band, and the (ν₁ + ν₃ + ν₅)¹ band, which gains its intensity through Coriolis resonance with 2ν₁. Centers of unblended lines are determined with an accuracy of approximately 10 MHz.     

Derivation of microscopic unified Bohr–Mottelson rotational model

In a previous article, we derived a microscopic version of the phenomenological Bohr–Mottelson unified rotational model for rotation about a single axis. In this article, we generalize the derivation to that for rotation about all the three axes. As in the previous derivation, we apply the nuclear Hamiltonian directly to the rotational-model wavefunction instead of using the usual canonical transformation. In this way, we avoid using redundant coordinates or imposing any constraints on the rotationally-invariant rotational-model intrinsic wavefunction. We show that, in the transformed nuclear Schrödinger equation, the Coriolis coupling term vanishes exactly only for a choice of the rotational-model Euler angles that is consistent with angle-angular momentum commutation relation and rotational invariance of the intrinsic wavefunction. For this choice of the Euler angles, the kinematic moment-of-inertia tensor, collective-rotation velocity field, and flow vorticity have the rigid-flow characteristics. This quantum rigid flow reduces to irrotational free-vortex flow in the limit of a single particle. We derive a microscopic effective rotation-intrinsic unified Schrödinger equation for the states of a rotational band that reduces to the phenomenological, unified, tri-axial quantum rigid-rotor model in the limit that the off-diagonal elements of the kinematic inertia tensor operator can be neglected. The model derivation shows that a multi-fermion system with unpaired or paired (quasi) particles rotates rigidly and a single-particle system rotates irrotationally if the intrinsic system is rotationally invariant.     

High resolution analysis of the ethylene-1-C spectrum in the 8.4-14.3-μm region

Fourier transform spectra of mono-¹³C ethylene have been recorded in the 8.4-14.3-μm spectral region (700-1190 cm⁻¹) using a Bruker 120 HR interferometer at a resolution of 0.0017 cm⁻¹ allowing the extensive study of the set of resonating states {10¹, 8¹, 7¹, 4¹, 6¹}. Due to the high resolution available as well as the extended spectral range involved in this study, a much larger set of line assignments are now available. The present analysis has lead to the determination of more accurate spectroscopic constants, including interaction constants, than were obtained in earlier studies. In particular, the following band centers were derived: ν₀(ν₁₀) = 825.40602(30) cm⁻¹, ν₀(ν₈) = 932.19572(15) cm⁻¹, ν₀(ν₇) = 937.44452(10) cm⁻¹, ν₀(ν₄) = 1025.6976(14) cm⁻¹. Finally a synthetic spectrum was generated leading to the assignment of a number of ¹³C¹²CH₄ lines observed in an earlier heterodyne spectroscopic study.