Zeeman transitions in deuterium atoms induced by ultra-relativistic electrons

We present data showing hyperfine transitions in an atomic deuterium beam induced by the (476 MHz) radio-frequency field of a 704 MeV electron beam in a storage ring. A polarized deuterium beam, produced in an atomic beam source, was crossed with a stored electron beam and analyzed with a Breit--Rabi polarimeter. Electron-beam induced transitions were singled out by injecting different combinations of hyperfine states. Transition probabilities as high as 70% were measured at large currents (~ 100 mA). All possible deuterium transitions for a radio-frequency of 476 MHz were observed. In addition, a 1--6 transition resulting from the first harmonic (952 MHz) was observed. The effects of these transitions are of general importance for the polarized internal target technique applied in nuclear and particle physics experiments. The data are reasonably described by numerical estimates. The observed mechanism can be exploited to create nuclear polarized atoms when injecting electron polarized atoms with no net nuclear polarization into a storage cell. However, when nuclear polarized atoms are injected, care should be taken to avoid this mechanism, since it would result in depolarization of the atoms. The studies enabled us to choose the magnetic guide field during our spin-dependent electron--deuteron scattering experiments, such that electron-beam induced depolarizing effects were avoided. This revised version was published online in July 2006 with corrections to the Cover Date.     

The four-loop β-function in quantum chromodynamics

We present the analytical calculation of the four-loop QCD β-function within the minimal subtraction scheme.     

Future pathways for combinatorial chemistry

Summary Investment in combinatorial chemistry (combichem) in the pharmaceutical industry is being driven by the need for increased efficiency. Results from pioneers in the field have demonstrated where mixture or discrete compound synthesis is useful, and what mixture sizes and compound concentrations are appropriate. To make the techniques of combichem of general utility in drug discovery, a broad range of advances is still required. Conversion of organic chemistry to solid phase conditions is key, as are developments in linkers and resins. Library design methodology requires further development. Combinatorial biosynthesis of focused libraries of natural products holds great promise for capitalising on hardwon natural product leads. Miniaturisation of screens is required to reduce the cost of screening combinatorial libraries. Developments in the processes preceding and following synthesis are required to enable the flow of increased numbers of compounds without new bottlenecks developing. The impact of combinatorial chemistry will be greatly enhanced by synergy with ongoing parallel developments in genetic technologies, screening technologies and bioinformatics.     

On the behaviour of rubberlike materials in compression and shear

Summary The mechanical behaviour of rubberlike materials is modelled in a phenomenological approach using a strain-energy formulation. Nonhomogeneous shear experiments on solid rubber specimens have been carried out as well as simple elongation tests on the same rubber compound. The elongation tests have been used to determine the model constants. By a comparison between experiment and numerical simulation of the nonhomogeneous shear test the predictive capabilities of the Mooney-Rivlin, the Ogden and the Besseling model have been assessed for compression-shear deformation paths. An analytical study explains the numerically observed behaviour.

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Über das Verhalten von Gummimaterialien unter Druck und Schubverformungen

Übersicht Das mechanische Verhalten von Gummimaterialien wird phänomenologisch modelliert unter Anwendung einer Formänderungsenergiefunktion. Es sind nicht-homogene Schubversuche auf dreidimensionale Versuchsproben aus Gummi so wie auch einfache Verlängerungsversuche auf Gummiproben der gleichen Zusammenstellung durchgeführt worden. Die Verlängerungsversuche sind durchgeführt worden um die Stoffkennwerte feststellen zu können. In einer Vergleichung zwischen dem Experiment und der numerischen Simulation von nicht-homogenen Schubversuchen ist die Genauigkeit des Mooney-Rivlinschen Modells, des Ogdenschen Modells und des Besselingschen Modells für kombinierte Druck-Schubverformungen festgestellt worden. In einem analytischen Studium wird das numerisch betrachtete Verhalten auseinandergesetzt.

     

Asymptotics in the random assignment problem

Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710     

Factorisation in the ring of exponential polynomials

We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's factorisation theorem in modern notation and so generalised as to deal with polynomial coefficients as well as with several variables. We do this in the more general context of a group ring of a divisible torsion-free ordered abelian group over a unique factorisation domain.

     

How should one define a (weak) crystal?

We compare two proposals for the study of positional long-range order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only the first one allows for the consideration of molecular, as opposed to atomic, (weakly) periodic structures. We illustrate this point on the Thue-Morse system.