Negative molecular ions of azafullerenes and their hydrogenated derivatives

The formation and decay of negative molecular ions of azafullerenes and their hydrogenated derivatives are investigated by mass spectrometry. The mechanisms of resonant electron capture and the lifetimes of negative molecular ions with respect to the electron autodetachment in azafullerene molecules are discussed. A comparative analysis of the data obtained for azafullerenes and hydrogenated fullerene derivatives is carried out.     

The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

Skyrmion in nuclear matter

The properties of Skyrmions in finite nuclei are considered. The deformation effect is taken into account through the external-field-induced distortion of the profile function of a chiral field. The masses of classical Skyrmions and the distribution of their baryon number versus the Skyrmion position within a nucleus are discussed.     

Bis(μ6‐cis‐2,4,6,8,10,12,14,16‐octa­methyl­cyclo­octa­siloxane‐2,4,6,8,10,12,14,16‐octolato)octa­kis[(dimethyl­formamide)copper(II)] dimethyl­formamide solvate enclosing a pyrazine mol­ecule

The title compound, [Cu₈(C₈H₂₄O₂Si)₂(C₃H₇NO)₈]·C₄H₄N₂·C₃H₇NO, features a sandwich‐like cage enclosing a pyrazine mol­ecule, both situated on a centre of inversion. In addition, the crystal structure contains one dimethyl­formamide mol­ecule which is disordered over a centre of inversion. The copper layer, containing eight atoms, is located between two siloxanolate fragments. The whole structure of Cu atoms and siloxanolate rings is distorted by the pyrazine mol­ecule, leading to an oval form. As a result, the angles between the Cu atoms differ at the copper layer. The difference in the angles could lead to some deviations in the Cu–Cu exchange inter­actions within the copper ring, which is of inter­est for mol­ecular magnetism.     

Sub-Doppler and Doppler spectroscopy of DCN isotopomers in the terahertz region: ground and first excited bending states (v1v2v3)=(0 1 0)

The rotational spectra of the deuterium cyanide isotopic species DCN, D¹³CN, DC¹⁵N, and D¹³C¹⁵N were recorded in the vibrational ground and first excited bending state (v₂=1) up to 2 THz. The R-branch transitions from J=3←2 to J=13←12 were measured with sub-Doppler resolution. These very high resolution (∼70 kHz) and precise (±3-10 kHz) saturation dip measurements allowed for resolving the underlying hyperfine structure due to the ¹⁴N nucleus in DCN and D¹³CN for transitions as high as J=10←9. Additional high JR-branch (J=25←24 to J=28←27) transitions around 2 THz and direct l-type (ΔJ=0, J=19 to J=25) transitions from 66 to 118 GHz were recorded in Doppler-limited resolution. For the ground state of D¹³C¹⁵N, the J=1←0 transition was measured for the first time. The transition frequency accuracies for the other deuterated species were significantly improved. These new experimental data, together with the available infrared rovibrational data and previously measured direct l-type transitions, were subjected to a global least squares analysis for each isotopomer. This yielded precise sets of molecular constants for the ground and first excited vibrational states, including the nuclear quadrupole and magnetic spin-rotation coupling constants of the ¹⁴N nucleus for DCN and D¹³CN. The hyperfine structure due to the D, ¹³C, and ¹⁵N nuclei have not been resolved, but led to a broadening of the observed saturation dips.     

Ricci and Matter Collineations of Locally Rotationally Symmetric Space-Times

A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors. These results conclude a long due open problem, which has been considered many times partially in the literature.     

On the onset of separation in turbulent boundary layer flow over two-dimensional humps of various size

Summary The available laboratory data of turbulent boundary layer flow over two-dimensional obstacles have been examined in order to identify the parameters (such as the aspect ratio or the surface roughness) driving the onset of separation. A comparison with some linearized models suitable for atmospheric applications is also made. It results that i) the model response can be highly sensitive to the detailed shape of the obstacle; ii) the ratio between obstacle length and boundary layer thickness is relevant in determining the pressure perturbation near the surface; iii) the surface shear stress is poorly described in most cases and in particular in the obstacle wake.

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Riassunto I dati di laboratorio disponibili, relativi a strati limite turbolenti su ostacoli bidimensionali, sono stati esaminati al fine di identificare i parametri guida della separazione (quali la pendenza o la rugosità della superficie). Inoltre è stato fatto un confronto con i risultati di alcuni modelli linearizzati adatti per applicazioni atmosferiche. Ne risulta che i) la risposta del modello è molto sensibile alla forma dettagliata dell’ostacolo; ii) il rapporto fra la lunghezza dell’ostacolo e lo spessore dello strato limite turbolento incidente è importante nel determinare la perturbazione della pressione vicino alla superficie; iii) lo ?shear stress? superficiale non è riprodotto con accuratezza nella maggioranza dei casi, in particolare nella scia dell’ostacolo.

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Резюме Анализируются имеющиеся лабораторные данные по турбулентному течению в пограничном слое над двумерными препятствиями, чтобы идентифицировать параметры (такие как аспектное отношение или шероховатость поверхности), определяющие возникновение отрыва. Проводится сравнение с некоторыми линеаризованными моделями, удобными для атмосферных приложений. Получены следующие результаты: 1) модельный отклик может быть очень чувствительным к детальной форме препятствия; 2) отношение между длиной препятствия и толщиной поверхностного слоя является существенным при определении возмущения давления вблизи поверхности; 3) напряжение поверхностного сдвига плохо описывается в большинстве случаев и, в частности, в спутной струе.