Spin dynamics in crystalline and amorphous DyAg

Crystalline (cr-) Dyag [CsC] structure] orders antiferro-magnetically with T_N≅60K; amorphous (am-) DyAg ferro-magnetically with T_C≈-18K. We measured the longitudinal field (LF) μ⁺SR relaxation functions G_ZZ(t) for 5K<T<300K using surface muons. In the paramagnetic state. cr-DyAg gives an exponential G_ZZ (t) in the relaxation rate rising first slowly then more rapidlynear T_N; no decoupling is observed in LF up to 0.4T. In the ordered state we see a Lorentzian Kubo-Toyabe G_ZZ(t), becoming nearly static at the lowest temperatures. Its static width is very narrow (Δ≈-7 MHz), and full dceoupling is achieved here in 0.1 T. On approaching T_N, the fluctuation rate and the static width increase mootonically bt the field distribution remains Loratzian. A LF of 0.4T is then insufficient to quench the fast exponential relaxation. In paramagnetic am-DyAg, the μ⁺ depolarization is always much faster then in cr-DyAg. At lower temperatures it is better described by a root-exponential than an exponential G_ZZ(t). Below T_C an exponentially relaxing signal with 1/3 amplitude is seen. The decoupling effect of LF up to 0.4T was negligible at all temperatures.     

The effects of large oscillating fields on spin precession in magnetic resonance

Magnetic resonance of a spin system which is acted upon by a large near-resonance oscillating magnetic field transverse to a static field has been studied experimentally and theoretically for many years. The technique of DEMUR (Double Electron Muon Resonance) has many advantages for such studies. This paper will describe the results of an experiment to study the precession of the muonium triplet near magnetic resonance using DEMUR.     

Nonlinear corner‐cutting

This begins the study of a Riemannian generalization of a special case of algorithm I of Lane and Riesenfeld (1980), closely related to the de Casteljau algorithm (Goldman, 1989) for generating cubic polynomial curves. In our version, as in Shoemake's (1985), straight lines are replaced by geodesic segments. Our construction differs from Shoemake's in that it is a kind of stationary subdivision algorithm, defined by a recursive procedure, and it is not at all clear from the construction that a limiting curve q _∞ exists, much less that it is differentiable. Indeed, the aim of the present paper is to prove that q _∞ is differentiable and that the derivative is Lipschitz. The result is nontrivial: it is well‐known that stationary subdivision typically defines non‐differentiable curves (Cavaretta et al., 1991). On the other hand Shoemake's algorithm is non‐recursive and evidently defines a C ^∞ curve. Other approaches to splines on curved spaces are considered in (Barr et al., 1992; Chapman and Noakes, 1991; Duff, 1985; Gabriel and Kajiya, 1985; Noakes et al., 1989). This revised version was published online in June 2006 with corrections to the Cover Date.     

On the development of rational approximations incorporating inertial effects in coating and rimming flows: a multiple-scales approach

Analysis of thin-film rimming and coating flows is extendedto create a more general model, which can be identified as anew distinguished limit that has the work of certain previousstudies as specific limiting cases. Specifically, three-dimensionalflows under the influence of gravity are considered in whichthe Reynolds number is large enough to necessitate considerationof both inertial and centrifugal effects, along with those ofviscous, gravitational and surface-tension forces. Reductionof dimensionality is shown to be attainable within a systematic(multiple-timescale) asymptotic framework that encompasses allthese effects, leading to a two-dimensional formulation thatnot only is more general than many of the existing ones butalso represents a rational approximation in the sense that,in particular, the sizes of the dimensionless physical parametersto which it corresponds, together with the orders of magnitudeof the errors resulting from the reduction, can be preciselycharacterized.     

Determination of crystalline electric fields in RERh4B4 compounds

Using the Mössbauer effect of ¹⁵⁵Gd, the quadrupole interaction in GdRh₄B₄ has been measured, which yields the A⁰₂ term in the crystalline electric field Hamiltonian to be 1165 ± 100 K/a.u. Using this, the B⁰₂ terms for the other RERh₄B₄ (RE = Gd to Tm) have been deduced, and the physical properties predicted by the resulting Hamiltonian are compared with the experimental results.     

Silver sulphide growth on Ag(111): A medium energy ion scattering study

The interaction of S₂ with Ag(111) under ultra-high vacuum conditions has been investigated by medium energy ion scattering (MEIS). 100 keV He⁺ MEIS measurements provide a direct confirmation of a previous report, based on thermal desorption, that the growth of multilayer films of Ag₂S occurs through a continuous corrosion process. These films show a commensurate (√7 × √7)R19° unit mesh in low energy electron diffraction, consistent with the epitaxial growth of (111) layers of the high-temperature F-cubic phase of Ag₂S. The substantial range of co-existing film thicknesses found indicates that the growth must be in the form of variable-thickness islands. The use of 100 keV H⁺ incident ions leads to a very rapid decrease in the sulphide film thickness with increasing exposure that we attribute to an unusual chemical leaching, with implanted H atoms interacting with S atoms and desorption of H₂S from the surface.     

Compositional and structural medium energy ion scattering study of the temperature mediated diffusion determination at the Co/V interface in Co/V/MgO(100)

The impact of annealing at 300 °C on the elemental composition and the atomic structure of the Co/V interface in the 2.5 Å Co/70 Å V/MgO (100) system has been investigated by medium energy ion scattering (MEIS) using 100 keV He⁺ ions. By combining the experimental MEIS results with simulations we show that, while the Co/V interface is abrupt for the system kept at room temperature, annealing at 300 °C induces a strong interdiffusion leading to a Co_0.5V_0.5 surface bcc alloy with a high degree of disorder. Additionally, the MEIS data suggest that the surface of the annealed system is slightly rumpled by ~ 0.2 Å.     

Networks and closed balls

Neural networks calledtangent networks are constructed by explicit reference to the geometry of a set, and then blended intocascades which approximate characteristic functions of closed balls. In this way some known results about approximation by single hidden layer neural networks are re-proved in a very constructive and geometrical fashion.