Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

Three-dimensional imaging and detection efficiency performance of orthogonal coplanar CZT strip detectors

We report on recent three-dimensional imaging performance and detection efficiency measurements obtained with 5 mm thick prototype CdZnTe detectors fabricated with orthogonal coplanar anode strips. In previous work, we have shown that detectors fabricated using this design achieve both very good energy resolution and sub-millimeter spatial resolution with fewer electronic channels than are required for pixel detectors. As electron-only devices, like pixel detectors, coplanar anode strip detectors can be fabricated in the thickness required to be effective imagers for photons with energies in excess of 500 keV. Unlike conventional double-sided strip detectors, the coplanar anode strip detectors require segmented contacts and signal processing electronics on only one surface. The signals can be processed to measure the total energy deposit and the photon interaction location in three dimensions. The measurements reported here provide a quantitative assessment of the detection capabilities of orthogonal coplanar anode strip detectors

Fabrication and Optical Properties of a Fully Hybrid Epitaxial ZnO-Based Microcavity in the Strong Coupling Regime

In order to achieve polariton lasing at room temperature, a new fabrication methodology for planar microcavities is proposed: a ZnO-based microcavity in which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and in which two dielectric mirrors are used. This approach allows as to simultaneously obtain a high-quality active layer together with a high photonic confinement as demonstrated through macro-, and micro-photoluminescence ({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient polaritonic relaxation even at low excitation power.Comment: 12 pages, 3 figure

LO-phonon assisted polariton lasing in a ZnO based microcavity

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations

LUX -- A Laser-Plasma Driven Undulator Beamline

The LUX beamline is a novel type of laser-plasma accelerator. Building on the joint expertise of the University of Hamburg and DESY the beamline was carefully designed to combine state-of-the-art expertise in laser-plasma acceleration with the latest advances in accelerator technology and beam diagnostics. LUX introduces a paradigm change moving from single-shot demonstration experiments towards available, stable and controllable accelerator operation. Here, we discuss the general design concepts of LUX and present first critical milestones that have recently been achieved, including the generation of electron beams at the repetition rate of up to 5 Hz with energies above 600 MeV and the generation of spontaneous undulator radiation at a wavelength well below 9 nm.Comment: submitte

Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets

We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.Comment: 4 pages (revtex 4), 2 color EPS figure

Mixable Shuffles, Quasi-shuffles and Hopf Algebras

The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.Comment: 14 pages, no figure, references update

Anomalous f-electron Hall Effect in the Heavy-Fermion System CeTIn5_{5} (T = Co, Ir, or Rh)

The in-plane Hall coefficient $R_{H}(T)$ of CeRhIn$_{5}$, CeIrIn$_{5}$, and CeCoIn$_{5}$ and their respective non-magnetic lanthanum analogs are reported in fields to 90 kOe and at temperatures from 2 K to 325 K. $R_{H}(T)$ is negative, field-independent, and dominated by skew-scattering above $\sim$ 50 K in the Ce compounds. $R_{H}(H \to 0)$ becomes increasingly negative below 50 K and varies with temperature in a manner that is inconsistent with skew scattering. Field-dependent measurements show that the low-T anomaly is strongly suppressed when the applied field is increased to 90 kOe. Measurements on LaRhIn$_{5}$, LaIrIn$_{5}$, and LaCoIn$_{5}$ indicate that the same anomalous temperature dependence is present in the Hall coefficient of these non-magnetic analogs, albeit with a reduced amplitude and no field dependence. Hall angle ($\theta_{H}$) measurements find that the ratio $\rho_{xx}/\rho_{xy}=\cot(\theta_{H})$ varies as $T^{2}$ below 20 K for all three Ce-115 compounds. The Hall angle of the La-115 compounds follow this T-dependence as well. These data suggest that the electronic-structure contribution dominates the Hall effect in the 115 compounds, with $f$-electron and Kondo interactions acting to magnify the influence of the underlying complex band structure. This is in stark contrast to the situation in most $4f$ and $5f$ heavy-fermion compounds where the normal carrier contribution to the Hall effect provides only a small, T-independent background to $R_{H}.$Comment: 23 pages and 8 figure