Nuclear moments of the low abundant natural isotope 176Lu and hyperfine anomalies in the lutetium isotopes

The atomic beam magnetic resonance method combined with laser-induced state- and isotopeselective detection of metastable atoms has been used to investigate the hyperfine structure of the ²D ground multiplet in ¹⁷⁵Lu and ¹⁷⁶Lu. The analysis of the data yields not only accurate values for the hyperfine interaction constants, the nuclear magnetic dipole moment of ¹⁷⁵Lu, and the electronic g_J, factors, but also the first directly measured value of the nuclear magnetic dipole moment of the low abundant isotope ${}^{176}\text{Lu}\text{: μ}{}_{\mathrm{I}}\text{(}{}^{176}\text{Lu) = 3.1692 (45)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetic shielding). The spectroscopic quadrupole moment of ¹⁷⁶Lu was calculated from the ratio of the B-factors and the quadrupole moment of ${}^{175}\text{Lu}\text{: Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{176}\text{Lu}\text{) = 4.92 (3)}\text{b}$. Moreover, the magnetic hyperfine anomalies for the isotopic chain ^{175,176,176m,177}Lu were determined. A quadrupole hyperfine anomaly between ¹⁷⁵Lu and ¹⁷⁶Lu was not found when comparing the ratio of the B-factors in the states ${}^2\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$. From a comparison of the quadrupole moment of ¹⁷⁵Lu obtained from the hyperfine structure data and the quadrupole moment measured in muonic lutetium atoms semi-empirical Sternheimer shielding factors could be estimated.     

Games with frequency-dependent stage payoffs

Games with frequency-dependent stage payoffs (FD-games), are infinitely repeated non-cooperative games played at discrete moments in time called stages. The stage payoffs depend on the action pair actually chosen, and on the relative frequencies with which all actions were chosen before. We assume that players wish to maximize their expected (limiting) average rewards over the entire time-horizon. We prove an analogy to, as well as an extension of the (perfect) Folk Theorem. Each pair of rewards in the convex hull of all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Moreover, each pair of rewards in same set giving each player strictly more than the threat-point-reward, can be supported by a subgame-perfect equilibrium. Under a pair of jointly-convergent strategies, the relative frequency of each action pair converges in the long run. Received: March 2002/Revised: January 2003     

Comparative study of lattice‐Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction

In the present paper, a comparative study of numerical solutions for Newtonian fluids based on the lattice‐Boltzmann method (LBM) and the classical finite volume method (FVM) is presented for the laminar flow through a 4:1 planar contraction at a Reynolds number of value one, Re=1. In this study, the stress field for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM‐data use the evaluations of velocity gradients with finite differences. The stress field for both LBM and FVM is expressed in the present study in terms of the shear stress and the first normal stress difference. The lateral and axial profiles of the velocity, the shear stress and the first normal stress difference for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results. Copyright © 2004 John Wiley & Sons, Ltd.     

On the Origin and Energy of Triple Junction Defects Due to the Finite Length of Grain Boundaries

King [1] established that due to the discrete nature of their dislocation structure, finite length grain boundaries (GBs) in polycrystalline materials possess discrete values of misorientation angle. For a GB with a length that is not a multiple of the GB period, this leads to the formation of specific disclinations at their junctions with neighboring GBs, which compensate the difference between the misorientations of finite and infinite boundaries. In the present paper the origin of these compensating disclinations within GB triple junctions is elucidated and their strength is calculated using the disclination-structural unit model. It is shown that for a GB with length of about 10 nm the junction disclinations can have a strength value not more than 1°, in contrast to King's calculations that indicate much larger values. Elastic energies of triple junctions due to compensating disclinations are calculated for both equilibrium and non-equilibrium structures of a finite length GB, which differ by the position of the grain boundary dislocation network with respect to the junctions. The calculations show that triple junction energies are comparable to dislocation energies, and that compensating disclinations can play a significant role in the properties of nanocrystalline metals with grain sizes less than about 10 nm.     

Spatially periodic suspensions of convex particles in linear shear flows. I. Description and kinematics

Preparatory to a subsequent dynamical study in Part II, aimed at calculating the rheological properties of geometrically-ordered models of concentrated suspensions, a purely kinematical study is here presented of the motion of a mobile spatially periodic array of identical convex particles, typically spheres, participating in a macroscopically homogeneous linear shear flow to which the suspension as a whole is subjected. The geometrical configuration of such particle-lattice suspensions is shown to evolve temporally in a manner dependent upon the initial lattice configuration and the specific bulk shearing motion to which the suspension is subjected. Under certain circumstances the particle-lattice system is found to reproduce itself periodically in time—or, less stringently—“almost” periodically. Precise circumstances under which this occurs are exhaustively delineated for the entire class of two-dimensional isochoric spatially homogeneous shearing motions, parametrized by a scalar λ expressing the relative amounts of shear and vorticity present in the flow. This investigation is performed for both two- and three-dimensional lattices. (Eventual time averaging of the local, instantaneous, dynamical, interstitial fluid properties of these almost self-reproducing systems in Part II furnishes the rheological properties of the suspension.) Using concepts borrowed from Minkowski's geometry of numbers, calculations are outlined for establishing the maximum volume fraction of suspended particles that is kinematically possible for each shearing motion. This is observed to be always less than would obtain in a comparable static system.     

Cluster effects in the angular distribution of alphas scattered from34S

The addition of a resonance scattering contribution to the shape elastic scattering improves the fit in analysing experimental angular distributions. Spins from 7 to 10 ? characterize the resonances, which have a dominant influence on the six analysed angular distributions of 12.80 to 20 meV alpha particles elastically scattered from³⁴S. The relation between the energy of the resonances and their spin compares well with the results from alpha scattering from²⁸Si. As in the scattering from silicon, the occurrence of a dominating spins supports the assumption that they belong to cluster states formed when alpha particles hit the target nuclei.     

Analytic inequalities with applications to special functions

Sharp inequalities are derived for certain (polynomial-like) functions of the real variables p_i (i = 1(1)σ) by interpreting p_i as the probabilities that various switches be thrown in certain directions. Parameters m_v in the inequalities are at first taken to be integers; later the inequalities are established when m_v are arbitrary real numbers. The side condition ∑p_i = 1 occurs throughout analysis, so there are many corollaries. Examples of the inequalities established are

$\text{∑}\text{i=1}\text{σ}\text{(1?p}{}_{\mathrm{i}}{}^{\mathrm{m}}\text{)}{}^{\mathrm{m}}\text{>K?1,}$

valid ifm>1

$\text{∑}\text{j=0}\text{r}\text{n}\text{j}\text{p}{}^{\mathrm{jm}}\text{(1?p}{}^{\mathrm{m}}\text{)}{}^{\mathrm{m?j}}\text{+}\text{1?}\text{∑}\text{j=0}\text{r}\text{n}\text{j}\text{p}{}^{\mathrm{j}}\text{(1?p?s)}{}^{\mathrm{n?j}}{}^{\mathrm{m}}\text{> 1+s}{}^{\mathrm{<mtext>max</mtext><mtext>[m,n]</mtext>}}$

valid if m > 1, n > r + 1, 0 < p, s, p + s ? 1, and also valid if $\text{0 < m < 1, 0 < n < r + 1 (1 ? x)}{}^{\mathrm{u}}\text{+ x}{}^{\mathrm{<mtext>1</mtext><mtext>u</mtext>}}\text{< 1,}\text{if}\text{1}\text{2}\text{< x < 1, u > 1}$. (1.03)