Generalised Umbral Moonshine

Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the more general moonshine phenomenon which connects finite groups and distinguished modular objects. In this paper we introduce the notion of generalised umbral moonshine, which includes the generalised Mathieu moonshine [Gaberdiel M.R., Persson D., Ronellenfitsch H., Volpato R., Commun. Number Theory Phys. 7 (2013), 145-223] as a special case, and provide supporting data for it. A central role is played by the deformed Drinfel'd (or quantum) double of each umbral finite group $G$, specified by a cohomology class in $H^3(G,U(1))$. We conjecture that in each of the 23 cases there exists a rule to assign an infinite-dimensional module for the deformed Drinfel'd double of the umbral finite group underlying the mock modular forms of umbral moonshine and generalised umbral moonshine. We also discuss the possible origin of the generalised umbral moonshine

Measurement of the c-axis optical reflectance of AFe2_2As2_2 (A=Ba, Sr) single crystals: Evidence of different mechanisms for the formation of two energy gaps

We present the c-axis optical reflectance measurement on single crystals of BaFe$_2$As$_2$ and SrFe$_2$As$_2$, the parent compounds of FeAs based superconductors. Different from the ab-plane optical response where two distinct energy gaps were observed in the SDW state, only the smaller energy gap could be seen clearly for \textbf{E}$\parallel$c-axis. The very pronounced energy gap structure seen at a higher energy scale for \textbf{E}$\parallel$ab-plane is almost invisible. We propose a novel picture for the band structure evolution across the SDW transition and suggest different driving mechanisms for the formation of the two energy gaps.Comment: 4 page

Multiwavelength properties of a new Geminga-like pulsar: PSR J2021+4026

In this paper, we report a detailed investigation of the multiwavelength properties of a newly detected gamma-ray pulsar, PSR J2021+4026, in both observational and theoretical aspects. We firstly identify an X-ray source in the XMM-Newton serendipitous source catalogue, 2XMM J202131.0+402645, located within the 95% confidence circle of PSR J2021+4026. With an archival Chandra observation, this identification provides an X-ray position with arcsecond accuracy which is helpful in facilitating further investigations. Searching for the pulsed radio emission at the position of 2XMM J202131.0+402645 with a 25-m telescope at Urumqi Astronomical Observatory resulted in null detection and places an upper-limit of 0.1~mJy for any pulsed signal at 18~cm. Together with the emission properties in X-ray and gamma-ray, the radio quietness suggests PSR J2021+4026 to be another member of Geminga-like pulsars. In the radio sky survey data, extended emission features have been identified in the gamma-ray error circle of PSR J2021+4026. We have also re-analyzed the gamma-ray data collected by FERMI's Large Area Telescope. We found that the X-ray position of 2XMM J202131.0+402645 is consistent with that of the optimal gamma-ray timing solution. We have further modeled the results in the context of outer gap model which provides us with constraints for the pulsar emission geometry such as magnetic inclination angle and the viewing angle. We have also discussed the possibility of whether PSR J2021+4026 has any physical association with the supernova remnant G78.2+2.1 (gamma-Cygni).Comment: 11 pages, 14 figure

A block-diagonal structured model reduction scheme for power grid networks

We propose a block-diagonal structured model order reduction (BDSM) scheme for fast power grid analysis. Compared with existing power grid model order reduction (MOR) methods, BDSM has several advantages. First, unlike many power grid reductions that are based on terminal reduction and thus error-prone, BDSM utilizes an exact column-by-column moment matching to provide higher numerical accuracy. Second, with similar accuracy and macromodel size, BDSM generates very sparse block-diagonal reduced-order models (ROMs) for massive-port systems at a lower cost, whereas traditional algorithms such as PRIMA produce full dense models inefficient for the subsequent simulation. Third, different from those MOR schemes based on extended Krylov subspace (EKS) technique, BDSM is input-signal independent, so the resulting ROM is reusable under different excitations. Finally, due to its blockdiagonal structure, the obtained ROM can be simulated very fast. The accuracy and efficiency of BDSM are verified by industrial power grid benchmarks. © 2011 EDAA.published_or_final_versionDesign, Automation and Test in Europe Conference and Exhibition (DATE 2011), Grenoble, France, 14-18 March 2011. In Design, Automation, and Test in Europe Conference and Exhibition Proceedings, 2011, p. 44-4

Optical spectroscopy study on CeTe3_3: evidence for multiple charge-density-wave orders

We performed optical spectroscopy measurement on single crystal of CeTe$_3$, a rare-earth element tri-telluride charge density wave (CDW) compound. The optical spectra are found to display very strong temperature dependence. Besides a large and pronounced CDW energy gap being present already at room temperature as observed in earlier studies, the present measurement revealed the formation of another energy gap at smaller energy scale at low temperature. The second CDW gap removes the electrons near E$_F$ which undergo stronger scattering. The study yields evidence for the presence of multiple CDW orders or strong fluctuations in the light rare-earth element tri-telluride.Comment: 5 figure

DEM investigation of sand response during displacement pile installation

Previous experimental and numerical studies indicate that the stress state of sand at a specific depth changes significantly during the installation of a displacement pile. At a given depth level, the horizontal stress in sand increases as the end of pile approaches and reduces as the pile continues to penetrate and go past the sand element. This horizontal stress reversal, together with the large-strain deformation of the sand at the pile shaft, may cause a reduced accuracy in the calculation of pile capacity. In this paper, the micro-mechanical behaviour of sand developed around pile shaft during the installation of a closed-ended pile was studied using the two-dimensional Discrete Element Method (DEM). Sand assembly was modelled as uncrushable discs, and the closed-ended pile was modelled as a rigid clump which was made of a large number of overlapped discs with a fixed distance. The sand responses in terms of stress, strain and volume changes during the monotonic jacking of the closed-ended pile were investigated. Simulation results revealed micro-mechanical behaviours of the sand in both the interface zone “B” adjacent to the pile shaft and the far field zone “A” away from the pile. It was shown that the sand along the pile shaft at a small normalised distance to pile tip was subjected to a volume reduction as the pile goes past. As the pile drives deeper, the sand at a larger normalised distance to pile tip exhibited dilation. This captured process will give insights to the degradation of shaft friction at a given sand horizon

Eigenmodes of Decay and Discrete Fragmentation Processes

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which describes the process, into the biorthonormal basis of eigenmodes provided by the triangular matrix. When the transition rates have a scaling property in terms of mass ratios at binary fragmentation vertices, we obtain solvable models with explicit mathematical properties for the eigenmodes. A suitable continuous limit provides an interpolation between the solvable models. It gives a general relationship between the decay products and the elementary transition rates.Comment: 6 pages, plain TEX, 2 figures available from the author

A Survey on Approximation Mechanism Design without Money for Facility Games

In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games

Test of Factorization Hypothesis from Exclusive Non-leptonic B decays

We investigate the possibility of testing factorization hypothesis in non-leptonic exclusive decays of B-meson. In particular, we considered the non factorizable \bar{B^0} -> D^{(*)+} D_s^{(*)-} modes and \bar{B^0} -> D^{(*)+} (\pi^-, \rho^-) known as well-factorizable modes. By taking the ratios BR(\bar{B^0}-> D^{(*)+}D_s^{(*)-})/BR(\bar{B^0}-> D^{(*)+}(\pi^-,\rho^-)), we found that under the present theoretical and experimental uncertainties there's no evidence for the breakdown of factorization description to heavy-heavy decays of the B meson.Comment: 11 pages; submitted to PR