Disantangling the effects of Doppler velocity and primordial non-Gaussianity in galaxy power spectra

We study the detectability of large-scale velocity effects on galaxy clustering, by simulating galaxy surveys and combining the clustering of different types of tracers of large-scale structure. We employ a set of lognormal mocks that simulate a $20.000$ deg$^2$ near-complete survey up to $z=0.8$, in which each galaxy mock traces the spatial distribution of dark matter of that mock with a realistic bias prescription. We find that the ratios of the monopoles of the power spectra of different types of tracers carry most of the information that can be extracted from a multi-tracer analysis. In particular, we show that with a multi-tracer technique it will be possible to detect velocity effects with $\gtrsim 3 \sigma$. Finally, we investigate the degeneracy of these effects with the (local) non-Gaussianity parameter $f_{\rm NL}$, and how large-scale velocity contributions could be mistaken for the signatures of primordial non-Gaussianity.Comment: 17 pages, 25 figure

Ihara zeta functions for periodic simple graphs

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by Stark and Terras for finite graphs.Comment: 17 pages, 7 figures. V3: minor correction

A trace on fractal graphs and the Ihara zeta function

Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and Terras, Mizuno and Sato, to name just a few authors. Then, Clair and Mokhtari-Sharghi have studied zeta functions for infinite graphs acted upon by a discrete group of automorphisms. The main formula in all these treatments establishes a connection between the zeta function, originally defined as an infinite product, and the Laplacian of the graph. In this article, we consider a different class of infinite graphs. They are fractal graphs, i.e. they enjoy a self-similarity property. We define a zeta function for these graphs and, using the machinery of operator algebras, we prove a determinant formula, which relates the zeta function with the Laplacian of the graph. We also prove functional equations, and a formula which allows approximation of the zeta function by the zeta functions of finite subgraphs.Comment: 30 pages, 5 figures. v3: minor corrections, to appear on Transactions AM

Simulation of coalescence, break up and mass transfer in bubble columns by using the Conditional Quadrature Method of Moments in OpenFOAM

The evaluation of the mass transfer rates and the fluid-dynamics aspects of bubble columns are strongly affected by the intrinsic poly-dispersity of the gas phase, namely the different dispersed bubbles are usually distributed over a certain range of size and chemical composition values. In our previous work, gas-liquid systems were investigated by coupling Computational Fluid Dynamics with mono-variate population balance models (PBM) solved by using the quadrature method of moments (QMOM). Since mass transfer rates depend not only on bubble size, but also on bubble composition, the problem was subsequently extended to the solution of multi-variate PBM (Buffo et al. 2013). In this work, the conditional quadrature method of moments (CQMOM) is implemented in the open-source code OpenFOAM for describing bubble coalescence, breakage and mass transfer of a realistic partially aerated rectangular bubble column, experimentally investigated by Diaz et al.(2008). Eventually, the obtained results are here compared with the experimental data availabl

Time and energy-resolved two photon-photoemission of the Cu(100) and Cu(111) metal surfaces

We present calculations on energy- and time-resolved two-photon photoemission spectra of images states in Cu(100) and Cu(111) surfaces. The surface is modeled by a 1D effective potential and the states are propagated within a real-space, real-time method. To obtain the energy resolved spectra we employ a geometrical approach based on a subdivision of space into two regions. We treat electronic inelastic effects by taking into account the scattering rates calculated within a GW scheme. To get further insight into the decaying mechanism we have also studied the effect of the variation of the classical Hartree potential during the excitation. This effect turns out to be small.Comment: 11 pages, 7 figure

Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra

We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.Comment: 35 page

Thrust vector control requirements for launch vehicles using a 260-inch solid rocket first stage

Gimbaled nozzle and liquid injection thrust vector control requirements for solid rocket two stage launch vehicle