Production off2(1270) andf0(975) mesons by photons and hadrons of energy 65–175 GeV

Measurements are reported of inclusive production of -mesons in the beam fragmentation region in p, p andKp collisions. Results include a small but significant departure from VMD, and a pronounced rise in the/ ⁰ ratio with increasingp _T .     

A note on the dynamical zeta function of general toral endomorphisms

It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an elementary proof of this fact that extends to the case of general toral endomorphisms without change. The result is a closed formula that can be calculated by integer arithmetic only. We also address the functional equation and the relation between the Artin-Mazur and Lefschetz zeta functions.     

Diffraction of compatible random substitutions in one dimension

As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our revised approach yields explicit formulas for the pure point and the absolutely continuous parts, as well as a proof for the absence of singular continuous components. This approach is then extended to the family of random noble means substitutions and, as an example with an underlying 2-adic structure, to a locally randomised version of the period doubling chain. As a first step towards a more general approach, we interpret our findings in terms of a disintegration over the Kronecker factor, which is the maximal equicontinuous factor of a covering model set.     

Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum

We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the presence or absence of measure rigidity (restrictions on the set of possible shift-invariant ergodic measures to being those of algebraic origin), and different entropy ranks (which may be viewed as the maximal spatial dimension in which the system resembles an i.i.d. process). Despite these differences, it is shown that the resulting diffraction spectra are essentially indistinguishable, thus raising further difficulties for the inverse problem of structure determination from diffraction spectra. Some of them may be resolved on the level of higher-order correlation functions, which we also briefly compare.     

Nondestructive characterization of nanoscale layered samples

Multilayered samples consisting of Al, Co and Ni nanolayers were produced by MBE and characterized nondestructively by means of SRXRF, μ-XRF, WDXRF, RBS, XRR, and destructively with SIMS. The main aims were to identify the elements, to determine their purity and their sequence, and also to examine the roughness, density, homogeneity and thickness of each layer. Most of these important properties could be determined by XRF methods, e.g., on commercial devices. For the thickness, it was found that all of the results obtained via XRR, RBS, SIMS and various XRF methods (SRXRF, μ-XRF, WDXRF) agreed with each other within the limits of uncertainty, and a constant deviation from the presets used in the MBE production method was observed. Some serious preliminary discrepancies in the results from the XRF methods were examined, but all deviations could be explained by introducing various corrections into the evaluation methods and/or redetermining some fundamental parameters.     

A radial analogue of Poisson’s summation formula with applications to powder diffraction and pinwheel patterns

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.     

Deformation of Delone Dynamical Systems and Pure Point Diffraction

This article deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and aperiodic order, and important subclasses of them exhibit pure point diffraction spectra. We discuss the relevant framework and recall fundamental results and examples. In particular, we show that pure point diffraction is stable under equivariant local perturbations and discuss various examples, including deformed model sets. A key step in the proof of stability consists in transforming the problem into a question on factors of dynamical systems.     

Close-packed Dimers on the Line: Diffraction versus Dynamical Spectrum

The translation action of ℝ ^d on a translation bounded measure ω leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of ω, which is the carrier of the diffraction measure, lives on a subset of the dynamical spectrum. It is known that, under some mild assumptions, a pure point diffraction spectrum implies a pure point dynamical spectrum (the opposite implication always being true). For other systems, the diffraction spectrum can be a proper subset of the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with singular continuous diffraction) by van Enter and Miȩkisz (J. Stat. Phys. 66:1147–1153, 1992). Here, we construct a random system of close-packed dimers on the line that have some underlying long-range periodic order as well, and display the same type of phenomenon for a system with absolutely continuous spectrum. An interpretation in terms of ‘atomic’ versus ‘molecular’ spectrum suggests a way to come to a more general correspondence between these two types of spectra.