Rotational diffusion motion of PAA molecules in liquid crystal state

Inelastic neutron scattering measurements were performed on PAA in liquid crystal state. Interpretation of the quasi-elastic results was by the circular random walk model with N = 8 sites and K = 10¹⁰sec^-1 rate constant.     

Rotational Brownian motion of solute fluorescent molecules in liquids: Theory and experiment

The theories for the rotational Brownian motion of molecules in liquids were experimentally verified on the example of selected fluorescent probe molecules dissolved in various solvents. Agreement between theories and experimental results as well as some disagreements between them were found. The model of a coloured noise random torque has been employed to diminish the discrepancy between the Hubbard-Morita model of rotational Brownian motion of molecules in liquids and the experimental data. A mass drag effect due to the existence of viscosity shear waves is taken into account in the explanation of inertial effects in molecular motion in liquids. The hypothesis of microviscosity has been confirmed in some experimental situations.     

Rotational damping motion in nuclei

The recently proposed model to explain the mechanism of the rotational motion damping in nuclei is exactly solved. When compared with the earlier approximative solution, we find significative differences in the low excitation energy limit (i.e. ). For the strength functions we find distributions going from the Wigner semicircle through gaussians to Breit-Wigner shapes.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday. Work supported in part by the DFG and Cicyt, project PB88-0177     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.     

Rotational motion at finite temperature

Moments of inertia and rotational velocity fields are calculated in the cranking model for the harmonic oscillator and the Nilsson potential for even-even rare earth nuclei. By means of a temperature-averaging procedure these quantities are decomposed into a smooth and a shell-structure-dominated part. The results are in good agreement with the corresponding Strutinsky-averaged results. The velocity fields are analyzed in terms of vector spherical harmonics and compared to rigid flow. The smooth velocity fields reveal rigid flow in the nuclear interior; in the surface region a deviation from rigid flow occurs, giving rise to a backflow in the inner system. The temperature dependence of the smooth moments of inertia is approximated by a quadratic function.     

Rotational structures of long-range diatomic molecules

We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic molecule with -C _n /r ⁿ (n > 2) asymptotic interaction can have only 1, 2, and up to a maximum of n-2 rotational levels. A classification scheme of diatomic molecules is proposed, in which each class has a distinctive rotational structure and corresponds to different atom-atom scattering properties above the dissociation limit.Received: 15 June 2004, Published online: 28 September 2004PACS: 33.15.Mt Rotation, vibration, and vibration-rotation constants - 34.10. + x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) - 03.75.Nt Other Bose-Einstein condensation phenomena - 03.75.Ss Degenerate Fermi gases     

Rotational correlation functions of single molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict nonexponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.     

Rotational motion in sensorless freehand three-dimensional ultrasound

Freehand three-dimensional ultrasound is usually acquired with a position sensor attached to the ultrasound probe. However, position sensors can be expensive, obtrusive and difficult to calibrate. For this reason, there has been much research on alternative, image-based techniques, with in-plane motion tracked using conventional image registration methods, and out-of-plane motion inferred from the decorrelation between nearby B-scans. However, since out-of-plane motion is not the only source of decorrelation, image-based positions determined in this way suffer from cumulative drift errors. In this paper, we consider the effect of probe rotation on correlation and how this affects the position estimates. We then present a novel technique to compensate for out-of-plane rotations, by making use of orientation measurements from an unobtrusive sensor. Using simulations and in vitro experiments, we demonstrate that the technique is able to reduce the drift error in elevational positioning by 57% on average.     

Rotational relaxation of spherical-top molecules by atoms

A theoretical study of rotational relaxation of spherical-top molecules in an inert gas is presented. Under the assumption that the molecules and atoms collide as rough spheres, two previous theoretical methods obtained apparently conflicting results. These two methods are shown to be in agreement, the discrepancy being related to the definition of a fundamental relaxation time. When applied to the recent ultrasonic-absorption experiments, the relevant relaxation time is equal to that first reported by Widom. Throughout, the modified rough-sphere collision theory developed by Offerhaus is used. If ?_α is a reduced moment of inertia, defined by $\text{?}{}_{\mathrm{\alpha }}\text{= I/μσ}{}^2{}_{\mathrm{\alpha \beta }}$, where I is the moment of inertia of the rotating molecule, μ is the reduced mass of the atom-molecule pair, and σ_αβ is the sum of the atomic and molecular radii, then N_rot, the number of collisions suffered by each molecule in a time equal to the relaxation time, is $\text{N}{}_{\mathrm{rot}}\text{=}\text{3}\text{4}\text{(1 + ?}{}_{\mathrm{\alpha }}\text{)}{}^2\text{/?}{}_{\mathrm{\alpha }}\text{(1 ? cos φ)}$. Here φ is a parameter related to the rotation of a particular relative velocity vector, and ranges from zero (smooth spheres) to л (rough spheres). A correction to this result related to the attractive potential between atoms and molecules is obtained by multiplying N_rot by the factor exp (?ε/k_BT), in which ε is the depth of the attractive potential well, k_B is Boltsmann's constant and T is the temperature. Values for N_rot are tabulated for a variety of spherical-top molecule-inert gas systems.     

Rotational instability of filamentary crystals undergoing plastic deformation

We investigated the kinetics of spontaneous torsion in filamentary crystals during plastic deformation by a tensile load. The nature of the observed effect is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 76–81, August, 1988.     

Rotational and vibrational excitation of sputtered diatomic molecules

The rotational and vibrational level population distributions of ground and electronically excited states of several homonuclear and heteronuclear molecules are calculated for direct ejection, association, and associative ionization mechanisms of molecule sputtering. The cascade properties, formation mechanism, initial atom separation, and axis orientation to the surface are clearly reflected in the sputtered molecule distributions. In general, extensive non-Boltzmann rotational and vibrational distributions are predicted. The probability that an atom pair survives the ejection, for typical sputtering parameters, is high; approximately 50% for homonuclear molecules to near 100% for hydrides. The predictions are compared with experimental optical emission spectra in the accompanying paper.     

Rotational solutions under the new theory of motion

The author recently introduced a new theory of motion which resolves several problems in the philosophy of physics and mathematics by replacing the continuum with nonvanishing time. Nonvanishing time means that the magnitude of an instant does not have the functional properties of zero, even though it may be very small. As a result, joint functions of time, such ass=vt, vary as the other terms even when time is instantaneous. Hence size (vdt or instantaneous position) is increasing as velocity. This paper presents some quantitative solutions to the above for the case in which a point of massm is resolving in a perfect circle with uniform speedv=r. The magnitude of an instantdt — the minimum time for real events—is found by obtaining the magnitude of the arcds along which the rotating point is distributed overdt time. Under the Heisenberg uncertainty principle this turns out to beds ²=h(m)^–1. If the de Broglie equation and Einstein's two equations for photon energy are introduced, then in generalds ²=r. Under the quantum mechanical definition of orbital angular momentum r ^–1=2n ^–1, wheren is the integral scalar for. Hence there is an asymmetry on the right side of the last expression fords, and the ratio ofds to the circumference of the circle is (2n)^–1/2.     

Mössbauer effect studies of the plastic phase transition in Sn(CH3)4-doped neopentane

Mössbauer effect measurements were performed on Sn(CH₃)₄-doped samples of neopentane in the vicinity of the plastic phase transition temperature of neopentane. A sharp change in the recoilless fraction was observed near the transition temperature. No changes in the linewidth and isomer shift were observed.     

Rotational energies of plar symmetric-top molecules in high electric fields

A method based on hypervirial theorems and perturbation theory is developed for calculating rotational energies of polar symmetric-top molecules in uniform electric fields. This procedure also provides expectation values of other physical observables such as the effective dipole moment.     

Rotational selection rules for doublet-quartet transitions in asymmetric top molecules

Selection rules on the rotational structure of doublet-quartet transitions in asymmetric top molecules are discussed on the basis of the spin-orbit coupling mechanism, rather than by symmetry arguments, and some additional rules are found with respect to a previous work. In the case that the combining doublet and quartet states are appreciably mixed only with levels directly connected to them by the spin-orbit operator, it turns out that, except for the very low values of the rotational quantum numbers, branches with |ΔN ? ΔJ| > 1 are essentially forbidden. Thus, branches with ΔN = ± 3 (T and N branches) are not expected to be observable. In this case, it is found also that in a high magnetic field transitions with ΔM_s = ±2 are forbidden, and only ΔM_s = 0, ±1 bands are expected to occur. All these restrictions are removed if the combining states are also appreciably contaminated by states indirectly connected to them by the spin-orbit operator, through intermediate levels.