A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Sch\"afer parameterisations of real hyperbolic domains

Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Sch\"afer type of parameterisations of real hyperbolic O(m,n)-invariant domains remains a challenging problem. We show that a naive choice of the volume element invalidates the transformation, and put forward a conjecture about the correct form which ensures the desired structure. The conjecture is supported by complete analytic solution of the problem for groups O(1,1) and O(2,1), and by a method combining analytical calculations with a simple numerical evaluation of a two-dimensional integral in the case of the group O(2,2).Comment: Published versio

TDLAS Detection of propane and butane gas over the near-infrared wavelength range from 1678nm to 1686nm

It is important in the petrochemical industry that there are high sensitivity, high accuracy, low-power consumption and intrinsically safe methods for the detection of propane, butane and their gas mixtures, to provide early warning of potential explosion hazards during both storage and transportation of oil and gas. This paper proposes a 'proof of principle' method for the detection of propane and butane using a Tunable Diode Laser Absorption Spectroscopy (TDLAS) technique over the near-infrared wavelength range from 1678nm to 1686nm. This method is relatively inexpensive to implement and is thus more practical, compared with detection methods using wavelengths further into the infra-red, near 3.3μm. The minimum detectable concentration was found to be low as 300ppm for propane or butane. Importantly, the relative measurement errors were all below 3% LEL, which meets the requirements from the petrochemical and oil-gas storage and transportation industries for a field-based system for monitoring of combustible gases

Metal-insulator transition in half-filling two-orbital Hubbard model on triangular lattice

We have investigated the half-filling two-orbital Hubbard model on a triangular lattice by means of the dynamical mean-field theory (DMFT). The densities of states and optical conductivity clearly show the occurence of metal-insulating transition (MIT) at U$_{c}$, U$_{c}$=18.2, 16.8, 6.12 and 5.85 for J=0, 0.01U, U/4 and U/3, respectively. The distinct continuities of double occupation of electrons, local square moments and local susceptibility of the charge, the spin and the orbital at J > 0 suggest that the MIT is the first-order; however at J=0, the MIT is the second-order in the half-filling two-orbital Hubbard model on triangular lattices. We attribute the first-order nature of the MIT to the low symmetry of the systems with finite Hund's coupling J.Comment: 5 figures,13 pages, published versio

Phantom Mimicry on the Normal Branch of a DGP-inspired Braneworld Scenario with Curvature Effect

It has been shown recently that phantom-like effect can be realized on the normal branch of the DGP setup without introduction of any phantom matter neither in the bulk nor on the brane and therefore without violation of the null energy condition. It has been shown also that inclusion of the Gauss-Bonnet term in the bulk action modifies this picture via curvature effects. Here, based on the Lue-Starkman conjecture on the dynamical screening of the brane cosmological constant in the DGP setup, we extend this proposal to a general DGP-inspired $f(R,\phi)$ model that stringy effects in the ultra-violet sector of the theory are taken into account by inclusion of the Gauss-Bonnet term in the bulk action. We study cosmological dynamics of this setup, especially its phantom-like behavior and possible crossing of the phantom divide line especially with a non-minimally coupled quintessence field on the brane. In this setup, scalar field and curvature quintessence are treated in a unified framework.Comment: 25 Figures, To appear in MPL

Study of quasi-distributed optical fiber methane sensors based on laser absorption spectrometry

The coal industry plays an important role in the economic development of China. With the increase of coal mining year by year, coal mine accidents caused by gas explosion also occur frequently, which poses a serious threat to the life safety of absenteeism and national property safety. Therefore, high-precision methane fiber sensor is of great significance to ensure coal mine safety. This paper mainly introduces two kinds of quasi-distributed gas optical fiber sensing systems based on laser absorption spectroscopy. The gas fiber optic sensor based on absorption spectrum has high measurement accuracy, fast response and long service life. One is quasi-distributed optical fiber sensing system based on spatial division multiplexing (SDM) technology and the other is quasi-distributed optical fiber sensing system based on optical time domain reflection and time division multiplexing(TDM) technology

Coal mine low power laser methane detection and alarm instrument

At present, the portable carrier catalytic methane detection and alarm instrument for coal mine generally has many problems, such as high power consumption, short standby time, low detection accuracy, few parameters and single function, which can not meet the rapid development needs of mine safety. In this paper, a low power portable laser methane detection and alarm instrument based on tunable laser absorption spectroscopy (TDLAS) is designed. The instrument can detect methane concentration, ambient temperature and ambient pressure at the same time. It has the functions of sound and light alarm, historical data storage and query, and integrates Wi-Fi to realize data wireless transmission. The instrument can work continuously for 36 hours, and the response time is less than 15 seconds. It has the function of self-diagnosis. The overall performance of the instrument has been greatly improved compared with the traditional mine methane portable instrument. A mobile methane alarm Internet of things(IOT) system for coal mine based on portable instrument has been developed, which realizes real-time upload of data and cloud analysis, makes the traditional mine gas monitoring and control system powerfully supplemented, greatly improves the detection level of coal mine gas, and has broad application prospects

Universal scaling in sports ranking

Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth. Herewith, we study a specific kind, sports ranking systems in which players' scores and prize money are calculated based on their performances in attending various tournaments. A typical example is tennis. It is found that the distributions of both scores and prize money follow universal power laws, with exponents nearly identical for most sports fields. In order to understand the origin of this universal scaling we focus on the tennis ranking systems. By checking the data we find that, for any pair of players, the probability that the higher-ranked player will top the lower-ranked opponent is proportional to the rank difference between the pair. Such a dependence can be well fitted to a sigmoidal function. By using this feature, we propose a simple toy model which can simulate the competition of players in different tournaments. The simulations yield results consistent with the empirical findings. Extensive studies indicate the model is robust with respect to the modifications of the minor parts.Comment: 8 pages, 7 figure

On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values

Given any fixed $N \times N$ positive semi-definite diagonal matrix $G\ge 0$ we derive the explicit formula for the density of complex eigenvalues for random matrices $A$ of the form $A=U\sqrt{G}$} where the random unitary matrices $U$ are distributed on the group $\mathrm{U(N)}$ according to the Haar measure.Comment: 10 pages, 1 figur

Validity of abundances derived from spaxel spectra of the MaNGA survey

We measured the emission lines in the spaxel spectra of MaNGA galaxies in order to determine the abundance distributions therein. It has been suggested that the strength of the low-ionization lines, R_2, N_2, and S_2 may be increased (relative to Balmer lines) in (some) spaxel spectra of the MaNGA survey due to a contribution of the radiation of the diffuse ionized gas. Consequently, the abundances derived from the spaxel spectra through strong-line methods may suffer from large errors. We examined this expectation by comparing the behaviour of the line intensities and the abundances estimated through different calibrations for slit spectra of HII regions in nearby galaxies, for fibre spectra from the SDSS, and for spaxel spectra of the MaNGA survey. We found that the S_2 strength is increased significantly in the fibre and spaxel spectra. The mean enhancement changes with metallicity and can be as large as a factor of 2. The mean distortion of R_2 and N_2 is less than a factor of 1.3. This suggests that Kaufmann et al.'s demarcation line between AGNs and HII regions in the BPT diagram is a useful criterion to reject spectra with significantly distorted strengths of the N_2 and R_2 lines. We find that the three-dimensional R calibration, which uses the N_2 and R_2 lines, produces reliable abundances in the MaNGA galaxies. The one-dimensional N2 calibration produces either reliable or wrong abundances depending on whether excitation and N/O abundance ratio in the target region (spaxel) are close to or differ from those parameters in the calibrating points located close to the calibration relation. We then determined abundance distributions within the optical radii in the discs of 47 MaNGA galaxies. The optical radii of the galaxies were estimated from the surface brightness profiles constructed based on the MaNGA observations.Comment: 19 pages, 15 figures, accepted for publication in A&