Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify the posets for which equality holds.Comment: 13 pages, 1 figure; v2: corrected typos; v3: corrected typos and improved formatting; v4: to appear in Order; v5: corrected typos; v6: updated author email addresse

Design optimization of meta-material transmission lines for linear and non-linear microwave signal processing

The possibility to use CRLH (Composite Right-/Left-Handed) cells to realize both distributed wide-band filters for linear signal processing and non-linear devices like frequency doublers is investigated analytically and numerically. Full-wave electromagnetic simulations are performed for the filtering structure by means of a commercial software package and confirm the validity of the analytic results. Numerical results for CRLH NLTL (Non-Linear Transmission Line) obtained by using the Microwave Office are discussed, providing design considerations about the synthesis of such a component

Invariant Peano curves of expanding Thurston maps

We consider Thurston maps, i.e., branched covering maps $f\colon S^2\to S^2$ that are postcritically finite. In addition, we assume that $f$ is expanding in a suitable sense. It is shown that each sufficiently high iterate $F=f^n$ of $f$ is semi-conjugate to $z^d\colon S^1\to S^1$, where $d$ is equal to the degree of $F$. More precisely, for such an $F$ we construct a Peano curve $\gamma\colon S^1\to S^2$ (onto), such that $F\circ \gamma(z) = \gamma(z^d)$ (for all $z\in S^1$).Comment: 63 pages, 12 figure

Baby MIND Experiment Construction Status

Baby MIND is a magnetized iron neutrino detector, with novel design features, and is planned to serve as a downstream magnetized muon spectrometer for the WAGASCI experiment on the T2K neutrino beam line in Japan. One of the main goals of this experiment is to reduce systematic uncertainties relevant to CP-violation searches, by measuring the neutrino contamination in the anti-neutrino beam mode of T2K. Baby MIND is currently being constructed at CERN, and is planned to be operational in Japan in October 2017.Comment: Poster presented at NuPhys2016 (London, 12-14 December 2016). 4 pages, LaTeX, 7 figure

Baby MIND: A magnetised spectrometer for the WAGASCI experiment

The WAGASCI experiment being built at the J-PARC neutrino beam line will measure the difference in cross sections from neutrinos interacting with a water and scintillator targets, in order to constrain neutrino cross sections, essential for the T2K neutrino oscillation measurements. A prototype Magnetised Iron Neutrino Detector (MIND), called Baby MIND, is being constructed at CERN to act as a magnetic spectrometer behind the main WAGASCI target to be able to measure the charge and momentum of the outgoing muon from neutrino charged current interactions.Comment: Poster presented at NuPhys2016 (London, 12-14 December 2016). Title + 4 pages, LaTeX, 6 figure

Synchronization of the Distributed Readout Frontend Electronics of the Baby MIND Detector

Baby MIND is a new downstream muon range detector for the WGASCI experiment. This article discusses the distributed readout system and its timing requirements. The paper presents the design of the synchronization subsystem and the results of its test

Direct comparison of phase-space distributions of K- and K+ mesons in heavy-ion collisions at SIS energies - evidence for in-medium modifications of kaons ?

The ratio of K- to K+ meson yields has been measured in the systems RuRu at 1.69 A GeV, Ru+Zr at 1.69 A GeV, and Ni+Ni at 1.93 A GeV incident beam kinetic energy. The yield ratio is observed to vary across the measured phase space. Relativistic transport-model calculations indicate that the data are best understood if in-medium modifications of the kaons are taken into account.Comment: 14 pages including 3 figure

Charged pion production in 4496^{96}_{44}Ru+4496^{96}_{44}Ru collisions at 400A and 1528A MeV

We present transverse momentum and rapidity spectra of charged pions in central Ru + Ru collisions at 400$A$ and 1528$A$ MeV. The data exhibit enhanced production at low transverse momenta compared to the expectations from the thermal model that includes the decay of $\Delta(1232)$-resonances and thermal pions. Modification of the $\Delta$-spectral function and the Coulomb interaction are necessary to describe the detailed shape of the transverse momentum spectra. Within the framework of the thermal model, the freeze-out radii of pions are similar at both beam energies. The IQMD model reproduces the shapes of the transverse momentum and rapidity spectra of pions, but the predicted absolute yields are larger than in the measurements, especially at lower beam energy.Comment: 12 pages, 11 figure

Isospin dependence of relative yields of K+K^+ and K0K^0 mesons at 1.528 AGeV

Results on $K^+$ and $K^0$ meson production in $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions at a beam kinetic energy of 1.528$A$ GeV, measured with the FOPI detector at GSI-Darmstadt, are investigated as a possible probe of isospin effects in high density nuclear matter. The measured double ratio ($K^+/K^0$)$_{Ru}$/($K^+/K^0$)$_{Zr}$ is compared to the predictions of a thermal model and a Relativistic Mean Field transport model using two different collision scenarios and under different assumptions on the stiffness of the symmetry energy. We find a good agreement with the thermal model prediction and the assumption of a soft symmetry energy for infinite nuclear matter while more realistic transport simulations of the collisions show a similar agreement with the data but also exhibit a reduced sensitivity to the symmetry term.Comment: 5 pages, 3 figures. accepted for publication in Phys. Rev.