Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Received 31 January 2001 and Received in final form 26 June 2001     

First measurement of the ratio B(t --> Wb)/B(t --> Wq) and associated limit on the Cabibbo-Kobayashi-Maskawa element /V(tb)/

We present the first measurement of the ratio of branching fractions R identical withB(t-->Wb)/B(t-->Wq) from p_p collisions at sqrt[s] = 1.8 TeV. The data set corresponds to 109 pb(-1) of data recorded by the Collider Detector at Fermilab during the 1992-95 Tevatron run. We measure R = 0.94(+0.31)(-0.24)(stat+syst) or R>0.61 (0.56) at 90% (95)% C.L., in agreement with the standard model predictions. This measurement yields a limit on the Cabibbo-Kobayashi-Maskawa quark mixing matrix element /V(tb)/ under the assumption of three generations and unitarity.     

Measurement of d sigma/dM and forward-backward charge asymmetry for high-mass Drell-Yan e(+)e(-) pairs from pp macro collisions at square root of s = 1.8 TeV

We report on a measurement of the mass dependence of the forward-backward charge asymmetry, A(FB), and production cross section d sigma/dM for e(+)e(-) pairs with mass M(ee)>40 GeV/c(2). The data sample consists of 108 pb(-1) of pp macro collisions at square root of s = 1.8 TeV taken by the Collider Detector at Fermilab during 1992-1995. The measured asymmetry and d sigma/dM are compared with the predictions of the standard model and a model with an extra Z' gauge boson.     

Triple resonance investigation of F centres in BaFCl

Abstract

In BaFCl two types of F centres can be produced, where the electron occupies a Cl^? vacancy [F(Cl^?)-centres] or an F^? vacancy [F(F^?)-centres]. When producing F(F^?)-centres the simultaneous production of F(Cl^?)-centres cannot be avoided. Both ESR spectra overlap strongly. The ENDOR spectra contain very many lines of both centres and have a very complicated angular dependence. It is shown that the angular dependence of the ENDOR spectra of both F centres can be measured separately by applying a double ENDOR technique (called also Triple Resonance). The ratio of the signal heights of the ENDOR lines compared to the double ENDOR lines is characteristic for the neighbour shell to which the nuclei involved belong. The use of this effect for the analysis of the spectra and its explanation are discussed.     

Electron–electron interaction induced spin thermalization in quasi-low-dimensional spin valves

We study the spin thermalization, i.e., the inter-spin energy relaxation mediated by electron–electron scattering in small spin valves. When one or two of the dimensions of the spin valve spacer are smaller than the thermal coherence length, the direct spin energy exchange rate diverges and needs to be regularized by the sample dimensions. Here we consider two model systems: a long quasi-1D wire and a thin quasi-2D sheet.     

Collective shape oscillations of SiGe islands on pit-patterned Si(001) substrates: a coherent-growth strategy enabled by self-regulated intermixing

The shape of coherent SiGe islands epitaxially grown on pit-patterned Si(001) substrates displays very uniform collective oscillations with increasing Ge deposition, transforming cyclically between shallower "dome" and steeper "barn" morphologies. Correspondingly, the average Ge content in the alloyed islands also displays an oscillatory behavior, superimposed on a progressive Si enrichment with increasing size. We show that such a growth mode, remarkably different from the flat-substrate case, allows the islands to keep growing in size while avoiding plastic relaxation.     

Modelling and optimization of the Gosau hydro electric power system

This paper is concerned with the optimization of base load production of a real world storage power station system. Both mathematical models and numerical techniques are presented. Dynamic Programming is used for the numerical solution. A sensitivity analysis of the results is made and a discussion of the profit of the power plant company is given.     

A class of means and related inequalities

The aim of this paper is two-fold: First we describe a certain class of strictly positive, continuous functions u:I defined on certain intervals I]0,+[, and demonstrate that each function u of this class permits the definition of an associated mean M_u (a₁,...,a_n) for any finite number a₁,...,a_n of numbers in I. The arithmetic and the geometric mean are special cases of these u-means M_u. -Thereafter, we improve the classical inequality between the geometric and the arithmetic mean and derive from it a corresponding inequality between certain u-means and the arithmetic mean.     

Der Reaktionsmechanismus der allgemeinen Säure—Basen-Katalyse der Mutarotation der Glucose, 8. Mitt.: Die Aktivierungsenergie der heterogenen Kupfer-Katalyse der Glucose-Mutarotation (Kurze Mitteilung)

Ohne Zusammenfassung7. Mitt.:Hermann Schmid undG. Bauer, Mh. Chem.96, 1508 (1965); dort ältere Mitt. dieser Reihe zitiert.     

Rare-earth Metal Borosilicides R9Si15–xB3 (R = Tb,Yb): New Ordered Structures Derived from the AlB2 Structure Type

Two novel ternary borosilicides R₉Si_15–xB₃ (R = Tb, x = 1.80, R = Yb, x = 1.17) were synthesized from the initial elements using tin flux method. Their crystal structures were determined by means of X-ray single crystal diffraction. Both refer to space group R32, Z = 1: a = 6.668(2) Å, c = 12.405(4) Å [R₁ = 0.027, wR₂ = 0.031 for 1832 reflections with I_o > 2σ (I_o)] for Tb₉Si_15–xB₃, and a = 6.5796(3) Å, c = 12.2599(5) Å [R_F = 0.052, wR = 0.090 for 1369 reflections with I_o > 2σ (I_o)] for Yb₉Si_15–xB₃. The structures represent a new structure type, derived from that of AlB₂, with ordering in the metalloid sublattice resulting in distorted [Si₅B] hexagons. The presence or absence of boron in this ordered structure is discussed on the basis of difference Fourier syntheses, interatomic distances, structural analysis, and theoretical calculations in relation with the parent structures of the binaries AlB₂ and Yb₃Si₅ (Th₃Pd₅ type of structure). Theoretical calculations show substantial covalent interactions between the metal and nonmetal elements. The small percentage of silicon atoms, which are missing in these nonstoichiometric compounds, probably allows strengthening boron-metal and boron-silicon bonding.