Generalized Bruhat Cells and Completeness of Hamiltonian Flows of Kogan-Zelevinsky Integrable Systems

Let $G$ be any connected and simply connected complex semisimple Lie group, equipped with a standard holomorphic multiplicative Poisson structure. We show that the Hamiltonian flows of all the Fomin-Zelevinsky twisted generalized minors on every double Bruhat cell of $G$ are complete in the sense that all the integral curves of their Hamiltonian vector fields are defined on ${\mathbb{C}}$. It follows that all the Kogan-Zelevinsky integrable systems on $G$ have complete Hamiltonian flows, generalizing the result of Gekhtman and Yakimov for the case of $SL(n, {\mathbb{C}})$. We in fact construct a class of integrable systems with complete Hamiltonian flows associated to {\it generalized Bruhat cells} which are defined using arbitrary sequences of elements in the Weyl group of $G$, and we obtain the results for double Bruhat cells through the so-called open {\it Fomin-Zelevinsky embeddings} of (reduced) double Bruhat cells in generalized Bruhat cells. The Fomin-Zelevinsky embeddings are proved to be Poisson, and they provide global coordinates on double Bruhat cells, called {\it Bott-Samelson coordinates}, in which all the Fomin-Zelevinsky minors become polynomials and the Poisson structure can be computed explicitly.Comment: Title slightly changed; Section 1.3 expanded; some typos correcte

A scaling relation between merger rate of galaxies and their close pair count

We study how to measure the galaxy merger rate from the observed close pair count. Using a high-resolution N-body/SPH cosmological simulation, we find an accurate scaling relation between galaxy pair counts and merger rates down to a stellar mass ratio of about 1:30. The relation explicitly accounts for the dependence on redshift (or time), on pair separation, and on mass of the two galaxies in a pair. With this relation, one can easily obtain the mean merger timescale for a close pair of galaxies. The use of virial masses, instead of stellar masses, is motivated by the fact that the dynamical friction time scale is mainly determined by the dark matter surrounding central and satellite galaxies. This fact can also minimize the error induced by uncertainties in modeling star formation in the simulation. Since the virial mass can be read from the well-established relation between the virial masses and the stellar masses in observation, our scaling relation can be easily applied to observations to obtain the merger rate and merger time scale. For major merger pairs (1:1-1:4) of galaxies above a stellar mass of 4*10^10 M_sun/h at z=0.1, it takes about 0.31 Gyr to merge for pairs within a projected distance of 20 kpc/h with stellar mass ratio of 1:1, while the time taken goes up to 1.6 Gyr for mergers with stellar mass ratio of 1:4. Our results indicate that a single timescale usually used in literature is not accurate to describe mergers with the stellar mass ratio spanning even a narrow range from 1:1 to 1:4.Comment: accepted for publication in Ap

Simulation of an Axion Search Experiment

The resolution of the strong CP problem postulates a new dark matter candidate known as the axion. Axions can couple with photons in the presence of a strong magnetic field. Light shining through wall method (LSW) uses a lead wall inside a cavity with a strong magnetic field to coupled axions with photons then detect axions when the axions cross the lead wall and convert back to photons. The axion signal and thermal noise are simulated and by comparing the simulated signals after they have been rectified and integrated, the sensitivity of the planned experiment was determined

The multidimensional dependence of halo bias in the eye of a machine: a tale of halo structure, assembly and environment

We develop a novel approach in exploring the joint dependence of halo bias on multiple halo properties using Gaussian process regression. Using a $\Lambda$CDM $N$-body simulation, we carry out a comprehensive study of the joint bias dependence on halo structure, formation history and environment. We show that the bias is a multivariate function of halo properties that falls into three regimes. For massive haloes, halo mass explains the majority of bias variation. For early-forming haloes, bias depends sensitively on the recent mass accretion history. For low-mass and late-forming haloes, bias depends more on the structure of a halo such as its shape and spin. Our framework enables us to convincingly prove that $V_\mathrm{max}/V_\mathrm{vir}$ is a lossy proxy of formation time for bias modelling, whereas the mass, spin, shape and formation time variables are non-redundant with respect to each other. Combining mass and formation time largely accounts for the mass accretion history dependence of bias. Combining all the internal halo properties fully accounts for the density profile dependence inside haloes, and predicts the clustering variation of individual haloes to a $20\%$ level at $\sim 10\mathrm{Mpc}h^{-1}$. When an environmental density is measured outside $1\mathrm{Mpc}h^{-1}$ from the halo centre, it outperforms and largely accounts for the bias dependence on the internal halo structure, explaining the bias variation above a level of $30\%$.Comment: MNRAS accepte

Monolithic ultrasound fingerprint sensor.

This paper presents a 591×438-DPI ultrasonic fingerprint sensor. The sensor is based on a piezoelectric micromachined ultrasonic transducer (PMUT) array that is bonded at wafer-level to complementary metal oxide semiconductor (CMOS) signal processing electronics to produce a pulse-echo ultrasonic imager on a chip. To meet the 500-DPI standard for consumer fingerprint sensors, the PMUT pitch was reduced by approximately a factor of two relative to an earlier design. We conducted a systematic design study of the individual PMUT and array to achieve this scaling while maintaining a high fill-factor. The resulting 110×56-PMUT array, composed of 30×43-μm2 rectangular PMUTs, achieved a 51.7% fill-factor, three times greater than that of the previous design. Together with the custom CMOS ASIC, the sensor achieves 2 mV kPa-1 sensitivity, 15 kPa pressure output, 75 μm lateral resolution, and 150 μm axial resolution in a 4.6 mm×3.2 mm image. To the best of our knowledge, we have demonstrated the first MEMS ultrasonic fingerprint sensor capable of imaging epidermis and sub-surface layer fingerprints

Mississippi State Axion Search: A Light Shining though a Wall ALP Search

The elegant solutions to the strong CP problem predict the existence of a particle called axion. Thus, the search for axion like particles (ALP) has been an ongoing endeavor. The possibility that these axion like particles couple to photons in presence of magnetic field gives rise to a technique of detecting these particles known as light shining through a wall (LSW). Mississippi State Axion Search (MASS) is an experiment employing the LSW technique in search for axion like particles. The apparatus consists of two radio frequency (RF) cavities, both under the influence of strong magnetic field and separated by a lead wall. While one of the cavities houses a strong RF generator, the other cavity houses the detector systems. The MASS apparatus looks for excesses in RF photons that tunnel through the wall as a signature of candidate axion-like particles. The concept behind the experiment as well as the projected sensitivities are presented here.Comment: Xth Patras Workshop on Axions, WIMPs and WISPs; 4 Pages, 5 figure

Photometric Metallicity Calibration with SDSS and SCUSS and its Application to distant stars in the South Galactic Cap

Based on SDSS g, r and SCUSS (South Galactic Cap of u-band Sky Survey) $u$ photometry, we develop a photometric calibration for estimating the stellar metallicity from $u-g$ and $g-r$ colors by using the SDSS spectra of 32,542 F- and G-type main sequence stars, which cover almost $3700$ deg$^{2}$ in the south Galactic cap. The rms scatter of the photometric metallicity residuals relative to spectrum-based metallicity is $0.14$ dex when $g-r<0.4$, and $0.16$ dex when $g-r>0.4$. Due to the deeper and more accurate magnitude of SCUSS $u$ band, the estimate can be used up to the faint magnitude of $g=21$. This application range of photometric metallicity calibration is wide enough so that it can be used to study metallicity distribution of distant stars. In this study, we select the Sagittarius (Sgr) stream and its neighboring field halo stars in south Galactic cap to study their metallicity distribution. We find that the Sgr stream at the cylindrical Galactocentric coordinate of $R\sim 19$ kpc, $\left| z\right| \sim 14$ kpc exhibits a relative rich metallicity distribution, and the neighboring field halo stars in our studied fields can be modeled by two-Gaussian model, with peaks respectively at [Fe/H]$=-1.9$ and [Fe/H]$=-1.5$.Comment: 8 pages, 7 figures, Accepted for publication in MNRA