Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

Unitary Fermi Gas in a Harmonic Trap

We present an {\it ab initio} calculation of small numbers of trapped, strongly interacting fermions using the Green's Function Monte Carlo method (GFMC). The ground state energy, density profile and pairing gap are calculated for particle numbers $N = 2 \sim 22$ using the parameter-free "unitary" interaction. Trial wave functions are taken of the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that energies can be well fitted by the expression $a_{TF} E_{TF} + \Delta {\rm mod}(N,2)$ where $E_{TF}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\Delta$ is a pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\Delta= 0.7\pm 0.2\omega$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.Comment: 2 figures, 2 table

Ab initio study of a mechanically gated molecule: From weak to strong correlation

The electronic spectrum of a chemically contacted molecule in the junction of a scanning tunneling microscope can be modified by tip retraction. We analyze this effect by a combination of density functional, many-body perturbation and numerical renormalization group theory, taking into account both the non-locality and the dynamics of electronic correlation. Our findings, in particular the evolution from a broad quasiparticle resonance below to a narrow Kondo resonance at the Fermi energy, correspond to the experimental observations.Comment: 4 pages, 3 figure

New constraints on a light CP-odd Higgs boson and related NMSSM Ideal Higgs Scenarios

Recent BaBar limits on \br(\Upsilon(3S)\to \gam a\to \gam \tau^+\tau^-) and \br(\Upsilon(3S)\to \gam a\to \gam \mu^+\mu^-) provide increased constraints on the a b\anti b coupling of a CP-odd Higgs boson, $a$, with $m_a<M_{\Upsilon(3S)}$. We extract these limits from the BaBar data and compare to the limits previously obtained using other data sets, especially the CLEO-III \br(\Upsilon(1S)\to \gam\to\tau^+\tau^-) limits. Comparisons are made to predictions in the context of "ideal"-Higgs NMSSM scenarios, in which the lightest CP-even Higgs boson, $h_1$, can have mass below 105\gev (as preferred by precision electroweak data) and yet can escape old LEP limits by virtue of decays to a pair of the lightest CP-odd Higgs bosons, $h_1\to a_1a_1$, with $m_{a_1}<2m_B$. Most such scenarios with $m_{a_1}<2m_\tau$ are eliminated, but the bulk of the m_{a_1}>7.5\gev scenarios, which are theoretically the most favored, survive. We also outline the impact of the new ALEPH LEP results in the \epem\to Z+4\tau channel. For $\tan\beta\geq 3$, only NMSSM ideal Higgs scenarios with m_{h_1}\gsim 98\gev and $m_{a_1}$ close to $2m_B$ satisfy the ALEPH limits. For \tan\beta\lsim 2, the ALEPH limits are easily satisfied for the most theoretically preferred NMSSM scenarios, which are those with $m_{a_1}$ close to $2m_B$ and m_{h_1}\sim 90\gev-100\gev.Comment: 24 pages, 25 figures, paper updated to incorporate final ALEPH limits in Z+4\tau channel

A systematic study of Rayleigh-Brillouin scattering in air, N2 and O2 gases

Spontaneous Rayleigh-Brillouin scattering experiments in air, N2 and O2 have been performed for a wide range of temperatures and pressures at a wavelength of 403 nm and at a 90 degrees scattering angle. Measurements of the Rayleigh-Brillouin spectral scattering profile were conducted at high signal-to-noise ratio for all three species, yielding high-quality spectra unambiguously showing the small differences between scattering in air, and its constituents N2 and O2. Comparison of the experimental spectra with calculations using the Tenti S6 model, developed in 1970s based on linearized kinetic equations for molecular gases, demonstrates that this model is valid to high accuracy. After previous measurements performed at 366 nm, the Tenti S6 model is here verified for a second wavelength of 403 nm. Values for the bulk viscosity for the gases are derived by optimizing the model to the measurements. It is verified that the bulk viscosity parameters obtained from previous experiments at 366 nm, are valid for wavelengths of 403 nm. Also for air, which is treated as a single-component gas with effective gas transport coefficients, the Tenti S6 treatment is validated for 403 nm as for the previously used wavelength of 366 nm, yielding an accurate model description of the scattering profiles for a range of temperatures and pressures, including those of relevance for atmospheric studies. It is concluded that the Tenti S6 model, further verified in the present study, is applicable to LIDAR applications for exploring the wind velocity and the temperature profile distributions of the Earth's atmosphere. Based on the present findings, predictions can be made on the spectral profiles for a typical LIDAR backscatter geometry, which deviate by some 7 percent from purely Gaussian profiles at realistic sub-atmospheric pressures occurring at 3-5 km altitude in the Earth's atmosphere

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Isolated Galaxies versus Interacting Pairs with MaNGA

We present preliminary results of the spectral analysis on the radial distributions of the star formation history in both, a galaxy merger and a spiral isolated galaxy observed with MaNGA. We find that the central part of the isolated galaxy is composed by older stellar population ($\sim$2 Gyr) than in the outskirts ($\sim$7 Gyr). Also, the time-scale is gradually larger from 1 Gyr in the inner part to 3 Gyr in the outer regions of the galaxy. In the case of the merger, the stellar population in the central region is older than in the tails, presenting a longer time-scale in comparison to central part in the isolated galaxy. Our results are in agreement with a scenario where spiral galaxies are built from inside-out. In the case of the merger, we find evidence that interactions enhance star formation in the central part of the galaxy.Comment: 7 pages, 2 figures. Proceedings of the EWASS-2015 special session Sp3, accepted for publication in Special Issue "3D View on Interacting and Post-Interacting Galaxies from Clusters to Voids" of open access journal "Galaxies