Spin dynamics from time-dependent spin-density-functional theory

We derive the spin-wave dynamics of a magnetic material from the time-dependent spin-density-functional theory in the linear response regime. The equation of motion for the magnetization includes, besides the static spin stiffness, a "Berry curvature" correction and a damping term. A gradient expansion scheme based on the homogeneous spin-polarized electron gas is proposed for the latter two quantities, and the first few coefficients of the expansion are calculated to second order in the Coulomb interaction.     

Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

Stability and Morphodynamics

Linear and nonlinear aspects of the development of morphodynamical features of fluvial and coastal environments are reviewed. It is emphasized that, in spite of the as yet incomplete understanding of the mechanics of sediment transport, some essential mechanisms operating in morphodynamics have been recently clarified by employing classical tools of linear and weakly nonlinear stability theory.     

A comparison between the craig-cox and the kacker-okapuu methods of turbine performance prediction

Summary Two complete comprehensive loss correlations for estimating the efficienty of axial-flow turbines are examinated in this paper: the well-known Craig-Cox method, and the recent development of the Ainley-Mathieson method, presented by Kacker and Okapuu, which reproposes the validity of this approach.Firstly, a comparison is done by evaluating the losses in a number representative cascades, having various solidities, aspect ratios, Reynolds and Mach numbers. It is shown that the two methods are in good agreement for subsonic cascades having high flow coefficients, while significant differences are found in high deflection blades, especially for the secondary losses.In the second part, it is investigated how the choice of correlation affects the project of a turbine stage. A design procedure, automatically carried out by a computer program, was applied to a number of cases: the differences between the two solutions of the same project problem obtained by using the two correlations are discusses. Parameters like specific speed, expansion ratio and size parameter are used to generalize the results.

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Sommario In questo articolo vengono considerati due metodi per la valutazione completa delle perdite fluidodinamiche in turbine assiali: il primo, ben noto, è quello proposto da Craig e Cox, mentre il secondo rappresenta il recente sviluppo del metodo di Ainley e Mathieson, operato da Kacker e Okapuu a conferma della validità dell'approccio originale.Un primo confronto è stato effettuato valutando le perdite in alcune schiere tipiche, con diversi numeri di Reynolds e di Mach. Viene mostrato che i due metodi sono in buon accordo per schiere subsoniche aventi elevati coefficienti di flusso, mentre si rilevano differenze significative in pale ad alta deflessione, specialmente per ciò che riguarda le perdite secondarie.Nella seconda parte si è voluto indagare come la scelta di una o dell'altra correlazione di perdite possa influenzare il progetto di stadi di turbine. Un certo numero di stadi tipici è stato ottimizzato mediante un codice automatico: vengono discusse le differenze tra le due soluzioni dello stesso problema progettuale risultate dall'uso di ambedue le correlazioni. I risultati sono presentati in funzione di parametri quali il numero di giri caratteristico, il rapporto di espansione e il coefficiente di «taglia», nell'intento di generalizzare i risultati.

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Palladium(II) complexes with sulphonium ylides

Keto-stabilized sulphonium ylides displace styrene and benzonitrile from their adducts with PdCl₂ to give stable $\text{2}\text{1}$ ylidePdCl₂ complexes. Evidence is given for epimeric equilibrium between trans square-planar structures of these new complexes in solution.A $\text{1}\text{1}$ ylidePdI₂ complex, obtained from dimethylsulphonium methylide, is also described.     

Le equazioni diofanteeax 4-bx 2+1=□, 4x 4+x 2 y 2+4y 4=□.

Summary Si determinano tre classi di quartiche u²=ax⁴+1, a e b interi, b²−4a≠□ per le quali l'appartenenza di un punto razionale (x₀,y₀),x₀≠0 porta l'esistenza nella stessa quartica di infiniti punti razionali. Si dimostra pure che l'equazione 4x²+x²y²+4y⁴=□ non ammette soluzioni intere con |xy| > 1. A BeniaminoSegre nel suo 70^mo compleanno. Entrata in Redazione il 26 febbraio 1973.     

Enhancement of shake-up structure in alkali-metal-ion exchanged forms of α-Zr(HPO4)2 by sputtering

Mg Kα ESCA spectra of several α-Zr(PO₄)₂M₂ compounds (M = Li⁺, Na⁺, K⁺, Cs⁺) have been obtained. Satellite structure is observed at ～7–8 eV from the main P 2s peak (corresponding to ～15–16 eV from the main Zr 3d_{$\text{5}\text{2}$} peak). The intensity of the satellite depends on the counter-ion intercalated. For a given counter-ion it is strongly increased by sputtering, the rate of increase being also dependent on the counter-ion. This observation is interpreted mainly in terms of electron-defect formation similar to that involved in the formation of colour centres by radiation damage, and subsequent charge-transfer shake-up of the trapped electrons to the electron-deficient phosphorus or Zr(IV) centres.     

X-ray structure of trichloro-oxo-(N-pyridylmethylene-N′-salicyloylhydrazine-NO)molybdenum(V) · acetonitrile (1/1). An example of isomerization by complexation

Summary The synthesis, i.r. spectrum and x-ray crystal structure of the title, complex are described, Crystals are monoclinic space groupP 2₁/n, witha = 19.901(7),b = 13.163(8),c = 7.273(6) A, = 90.58(5)° Z = 4, The structure was solved from diffractometer data by direct methods and refined by least-squares techniques toR = 0.053 for 923 independent reflections. The complex has a distortedmer-octahedral geometry [Mo-O = 1,70(1), 2.15(1), Mo-Cl = 2.340(7), 1.352(7), 2.280(7), Mo-N = 2.19(2) A], The starting ligand Hsip, which is in theE configuration when free and in a number of metal complexes where it is terdentate, assumes here theZ configuration and is hiclentate.     

Carbon-13 nuclear magnetic resonance spectra. VIII—18α- and 18β-glycyrrhetic acid derivatives

The ¹³C NMR data of six pairs of 18α/18β-glycyrrhetic acid derivatives are presented. It is shown that the configuration at C-18 can easily be recognized by inspecting the chemical shifts of several characteristic carbons, e.g. C-12, C-13, C-18 and C-28. The shifts of these carbons originated by the change of the D/E ring junction proved to be largely independent of the substitution at C-3 and C-20.