Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Sommerfeld Enhancement from Multiple Mediators

We study the Sommerfeld enhancement experienced by a scattering object that couples to a tower of mediators. This can occur in, e.g., models of secluded dark matter when the mediator scale is generated naturally by hidden-sector confinement. Specializing to the case of a confining CFT, we show that off-resonant values of the enhancement can be increased by ~ 20% for cases of interest when (i) the (strongly-coupled) CFT admits a weakly-coupled dual description and (ii) the conformal symmetry holds up to the Planck scale. Larger enhancements are possible for lower UV scales due to an increase in the coupling strength of the tower.Comment: 17p, 2 figures; v2 JHEP version (inconsequential typo fixed, references added

Conformational landscapes of bimesogenic compounds and their implications for the formation of modulated nematic phases

The twist-bend phase (NTB) is most commonly observed in materials with a gross-bent shape: dimers; bent-cores; bent-oligomers. We had suggested previously that the bend-angle of such systems effectively dictates the relative thermal stability of the NTB phase. However, our earlier paper relied on the use of a single energy-minimum conformer and so failed to capture any information about flexibility and conformational distribution. In the present work, we revisit our hypothesis and examine a second set of dimers with varying linking groups and spacer composition. We have improved on our earlier work by studying the conformational landscape of each material, allowing average bend-angles to be determined as well as the conformer distribution. We observe that the stability of the NTB phase exhibits a strong dependence not only on the Boltzmann-weighted average bend-angle (rather than just a static conformer), but also on the distribution of conformers. To a lesser extent, the flexibility of the spacer appears important. Ultimately, this work satisfies both theoretical treatments and our initial experimental study and demonstrates the importance of molecular bend to the NTB phase

Secluded Dark Matter Coupled to a Hidden CFT

Models of secluded dark matter offer a variant on the standard WIMP picture and can modify our expectations for hidden sector phenomenology and detection. In this work we extend a minimal model of secluded dark matter, comprised of a U(1)'-charged dark matter candidate, to include a confining hidden-sector CFT. This provides a technically natural explanation for the hierarchically small mediator-scale, with hidden-sector confinement generating m_{gamma'}>0. Furthermore, the thermal history of the universe can differ markedly from the WIMP picture due to (i) new annihilation channels, (ii) a (potentially) large number of hidden-sector degrees of freedom, and (iii) a hidden-sector phase transition at temperatures T << M_{dm} after freeze out. The mediator allows both the dark matter and the Standard Model to communicate with the CFT, thus modifying the low-energy phenomenology and cosmic-ray signals from the secluded sector.Comment: ~50p, 8 figs; v2 JHEP versio

Combined Microscopy, Calorimetry and X-ray Scattering Study of Fluorinated Dimesogens

The material FDO11DFCB3 (compound 2 in this work) remains the only example of a liquid-crystalline material to exhibit a phase transition from the heliconical twist-bend phase into a lamellar smectic A mesophase, additionally this material exhibits a previously unidentified mesophase. We have prepared and characterised several homologues of this compound, with each material subjected to an in-depth analysis by optical microscopy, calorimetry and small angle X-ray scattering studies. Despite FDO11DFCB3 being similar in chemical structure to the novel materials presented herein its liquid-crystalline behaviour is rather different, indicating an unexpected sensitivity of the twist-bend phase to molecular structure

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

CMS Data Processing Workflows during an Extended Cosmic Ray Run

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