Influence of reduced working frequencies on the floating‐zone growth of silicon single crystals

Lowering the working frequency in the inductively heated floating zone growth of Si Single crystals will reduce the risk of arcing at the induction coil. This is of particular interest in the growth of large diameter crystals. In the current paper we present results from growth experiments at lower frequencies, 2 MHz and 1.7 MHz. It is found that the growth of dislocation‐free crystals is possible at these frequencies and cause distinct changes in the interface deflection and radial resistivity profiles. Results from numerical simulation of the melt flow at different frequencies are presented. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Matrix representations of split Bezoutians

Inverses of symmetric (or skewsymmetric) Toeplitz matrices as well as of centrosymmetric (or centro-skewsymmetric) Toeplitz-plus-Hankel matrices can be represented as sums of two split Bezoutians which are highly structured matrices since all of their rows and columns are symmetric or skewsymmetric vectors. Thus it is desirable to find matrix representations for split Bezoutians B. This is the main aim of the present paper.Recursion formulas for the entries of B are presented, bases of very simple split Bezoutians or of sparse matrices are constructed, and B is represented as a corresponding linear combination. Moreover, matrix representations of Gohberg/Semencul type are established.     

Radiative π0 photoproduction on protons in the Δ+ (1232) region

The reaction γp → pπ ⁰γ′ has been measured with the Crystal Ball/TAPS detectors using the energy-tagged photon beam at the electron accelerator facility MAMI-B. Energy and angular differential cross-sections for the emitted photon γ′ and angular differential cross-sections for the π⁰ have been determined with high statistics in the energy range of the Δ⁺ (1232)-resonance. Cross-sections and the ratio of the cross-section to the nonradiative process γp → pπ ⁰ are compared to theoretical reaction models, having the anomalous magnetic moment κ _Δ as free parameter. As the shape of the experimental distributions is not reproduced in detail by the model calculations, currently no extraction of κ _Δ is feasible.     

Rydberg trimers and excited dimers bound by internal quantum reflection

In a combined experimental and theoretical effort we report on two novel types of ultracold long-range Rydberg molecules. First, we demonstrate the creation of triatomic molecules of one Rydberg atom and two ground-state atoms in a single-step photoassociation. Second, we assign a series of excited dimer states that are bound by a so far unexplored mechanism based on internal quantum reflection at a steep potential drop. The properties of the Rydberg molecules identified in this work qualify them as prototypes for a new type of chemistry at ultracold temperatures.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.     

More on Electrostatic Models for Zeros of Orthagonal Polynomials

Representations for inverses of Toeplitz-plus-Hankel matrices and more general Bezoutians involving only discrete Hartley transforms and diagonal matrices are presented. Using these representations a column vector can be multiplied by the inverse of a Toeplitz-plus-Hankel matrix with the help of only 6 Hartley transforms plus O(n) operations. This complexity estimate is significantly better than previous ones.