A preliminary design method for axisymmetric turbomachinery disks based on topology optimization

The topology optimization can be used to obtain preliminary turbomachinery disk designs which meet strength requirement. In order to eliminate enclosed holes which challenge manufacturing processes and to ensure distinct solid-void interface in the optimal result obtained by the topology optimization, a density distribution function is introduced for each element column in the design domain. Then, a parameter in each function is used to determine the disk’s thickness at corresponding radial position by controlling element densities. Once thicknesses at all radial positions are optimized, the shape of disk is thus determined. In this way, the optimization problem can be simplified by using these parameters as design variables. Illustrative examples are carried out to demonstrate the effectiveness of the proposed method in designing both compressor disks and turbine disks in comparison to the software T-Axis Disk and shape optimization method.

The relation between Lyα absorbers and local galaxy filaments

Context. The intergalactic medium (IGM) is believed to contain the majority of baryons in the universe and to trace the same dark matter structure as galaxies, forming filaments and sheets. Lyα absorbers, which sample the neutral component of the IGM, have been extensively studied at low and high redshift, but the exact relation between Lyα absorption, galaxies, and the large-scale structure is observationally not well constrained. Aims. In this study, we aim at characterising the relation between Lyα absorbers and nearby over-dense cosmological structures (galaxy filaments) at recession velocities Δv ≤ 6700 km s−1 by using archival observational data from various instruments. Methods. We analyse 587 intervening Lyα absorbers in the spectra of 302 extragalactic background sources obtained with the Cosmic Origins Spectrograph (COS) installed on the Hubble Space Telescope (HST). We combine the absorption line information with galaxy data of five local galaxy filaments from the V8k catalogue. Results. Along the 91 sightlines that pass close to a filament, we identify 215 (227) Lyα absorption systems (components). Among these, 74 Lyα systems are aligned in position and velocity with the galaxy filaments, indicating that these absorbers and the galaxies trace the same large-scale structure. The filament-aligned Lyα absorbers have a ∼90% higher rate of incidence (d𝒩/dz = 189 for log N(H I) ≥ 13.2) and a slightly shallower column density distribution function slope (−β = −1.47) relative to the general Lyα population at z = 0, reflecting the filaments’ matter over-density. The strongest Lyα absorbers are preferentially found near galaxies or close to the axis of a filament, although there is substantial scatter in this relation. Our sample of absorbers clusters more strongly around filament axes than a randomly distributed sample would do (as confirmed by a Kolmogorov–Smirnov test), but the clustering signal is less pronounced than for the galaxies in the filaments.

Method for determining the two-dimensional current density distribution function over the radiating structure based on chiral metamaterials

The article is devoted to the development of a method of electrodynamic analysis and a two-dimensional mathematical model of strip radiating structures based on the apparatus of hypersingular equations in order to ensure the correct calculation of their characteristics when using relatively small computational resources. A system of hypersingular integral equations with respect to the unknown transverse and longitudinal components of the current density distribution functions is obtained. This system of hypersingular equations was solved using the collocation method, where Gaussian nodes (zeros of Legendre polynomials) were used as collocation points. This approach allows for faster convergence compared to uniform partitioning. Numerical results of calculations of current density distribution functions for various parameters of the radiating structure based on chiral metamaterials are obtained. It is shown that in the case of wide emitters, it is necessary to take into account both components of the current density distribution function. The advantage of this method in comparison with universal analogues is the ability to accurately calculate the characteristics of radiating structures based on chiral metamaterials with wide emitters.

The evolution of the low-density H i intergalactic medium from z = 3.6 to 0: Data, transmitted flux and H i column density*†‡

We present a new, uniform analysis of the H i transmitted flux (F) and H i column density ($N_{\rm{H\, {\small I}}}$) distribution in the low-density IGM as a function of redshift z for 0 < z < 3.6 using 55 HST/COS FUV (Δz = 7.2 at z < 0.5), five HST/STIS+COS NUV (Δz = 1.3 at z ∼ 1) and 24 VLT/UVES and Keck/HIRES (Δz = 11.6 at 1.7 < z < 3.6) AGN spectra. We performed a consistent, uniform Voigt profile analysis to combine spectra taken with different instruments, to reduce systematics and to remove metal-line contamination. We confirm previously known conclusions on firmer quantitative grounds in particular by improving the measurements at z ∼ 1. Two flux statistics at 0 < F < 1, the mean H i flux and the flux probability distribution function (PDF), show that considerable evolution occurs from z = 3.6 to z = 1.5, after which it slows down to become effectively stable for z < 0.5. However, there are large sightline variations. For the H i column density distribution function (CDDF, f ∝ $N_{\rm H\, {\small I}}^{-\beta }$) at $\log (N_{\rm{H\, {\small I}}}/1\, {\mathrm{cm}^{-2}})$ ∈ [13.5, 16.0], β increases as z decreases from β = 1.60 at z ∼ 3.4 to β = 1.82 at z ∼ 0.1. The CDDF shape at lower redshifts can be reproduced by a small amount of clockwise rotation of a higher-z CDDF with a slightly larger CDDF normalisation. The absorption line number per z (dn/dz) shows a similar evolutionary break at z ∼ 1.5 as seen in the flux statistics. High-$N_{\rm{H\, {\small I}}}$ absorbers evolve more rapidly than low-$N_{\rm{H\, {\small I}}}$ absorbers to decrease in number or cross-section with time. The individual dn/dz shows a large scatter at a given z. The scatter increases toward lower z, possibly caused by a stronger clustering at lower z.

Connecting cosmological accretion to strong Ly α absorbers

ABSTRACT We present an analytical model for the cosmological accretion of gas on to dark matter haloes, based on a similarity solution applicable to spherical systems. Performing simplified radiative transfer, we compute how the accreting gas turns increasingly neutral as it self-shields from the ionizing background, and obtain the column density, $N_{\rm H\,{\small I}}$, as a function of impact parameter. The resulting column-density distribution function (CDDF) is in excellent agreement with observations. The analytical expression elucidates (1) why haloes over a large range in mass contribute about equally to the CDDF as well as (2) why the CDDF evolves so little with redshift in the range z = 2–5. We show that the model also predicts reasonable damped Lyman-αabsorber(DLA) line widths (v90), bias, and molecular fractions. Integrating over the CDDF yields the mass density in neutral gas, $\Omega _{\rm H\,{\small I}}$, which agrees well with observations. $\Omega _{\rm H\,{\small I}}(z)$ is nearly constant even though the accretion rate on to haloes evolves. We show that this occurs because the fraction of time that the inflowing gas is neutral depends on the dynamical time of the halo, which is inversely proportional to the accretion rate. Encapsulating results from cosmological simulations, the simple model shows that most Lyman-limit systems and DLAs are associated with the cosmological accretion of gas on to haloes.

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory.

Detecting multiple DLAs per spectrum in SDSS DR12 with Gaussian processes

ABSTRACT We present a revised version of our automated technique using Gaussian processes (GPs) to detect damped Lyman α absorbers (DLAs) along quasar (QSO) sightlines. The main improvement is to allow our GP pipeline to detect multiple DLAs along a single sightline. Our DLA detections are regularized by an improved model for the absorption from the Lyman α forest that improves performance at high redshift. We also introduce a model for unresolved sub-DLAs that reduces misclassifications of absorbers without detectable damping wings. We compare our results to those of two different large-scale DLA catalogues and provide a catalogue of the processed results of our GP pipeline using 158 825 Lyman α spectra from SDSS data release 12. We present updated estimates for the statistical properties of DLAs, including the column density distribution function, line density (dN/dX), and neutral hydrogen density (ΩDLA).

Joint law of an Ornstein–Uhlenbeck process and its supremum

Let X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.