ON THE EVOLUTION OF LARGE SCALE STRUCTURES IN THREE-DIMENSIONAL MIXING LAYERS

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing lavers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were pi /2 - phi and pi /2 + phi, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge.

AN ESTIMATE OF THE EFFECTS OF LARGE SCALE STRUCTURES ON THE TURBULENT TRANSPORT PROCESSES NEAR WALL

Based on the three-term decomposition model for turbulent flows, the fundamental equations for quasi-periodic motions are obtained, and the approximate analytical solutions of these second-order nonlinear partial differential equations are derived by using the match method. The effects on the mo- mentum, heat and mass transport processes in the wall turbulent flows can be estimated approximately.

AN EXPERIMENTAL STUDY OF THE LARGE SCALE COHERENT STRUCTURES IN A FORCED FREE SHEAR LAYER

The dynamic characteristics of the large scale coherent structures in a forced free shear layer are experi- mentally studied by means of flow visualization. The quantitative measurements are acquired by the use of a LDV. It is shown that the development of the coherent structures can be greatly influenced by upstream artificial perturbations and as a result the mixing in the layer can be controlled. Like vortex merging, vortex splitting is also a common evolu- tion pattern in the development of the coherent structures.

THE EFFECTS OF VELOCITY RATIO ON THE LARGE SCALE COHERENT STRUCTURES IN FREE SHEAR LAYERS

The velocity ratio of a free shear layer has an important influence on the spatial development of the large scale coherent structures in the layer. In this study, numerical simulations are performed to get an insight into this problem. The obtained numerical results agree quite well with those of a linear inviscid stability theory and the available experimental data.

Classical Cosmology I. Anomalous Redshift for Galaxies in NED-D

Three mechanisms for an alternative to the Doppler effect as an explanation for the redshift are reviewed. A fourth mechanism is the attenuation of the light as given by the Beer-Lambert law. The average value of the Hubble constant is therefore derived by processing the galaxies of the NED-D catalog in which the distances are independent of the redshift. The observed anisotropy of the Hubble constant is reproduced by adopting a rim model, a chord model, and both 2D and 3D Voronoi diagrams.

Classical Cosmology III. Modified Tired Light and Distance Modulus for Supernovae

We analyze a simple model for tired light in a cosmological environment, a generalized model, and a spectroscopic model. The three models are tested on different compilations for the distance modulus of supernovae. The tests are negative for the simple tired light and the spectroscopic models, but positive for the generalized tired light model. The percentage error of the distance modulus for the generalized tired light model compared with the distance modulus of standard cosmology is less than one percent over the considered ranges in redshift.

Estimating the power spectrum of a discrete cosmic momentum field with fast Fourier transform

Fast Fourier transform based estimators are formulated for measuring momentum power spectra,including the auto power spectra of the momentum,the momentum divergence,and the cross spectrum of density fluctuation and momentum divergence.Algorithms using the third order Bettle-Lemariéscaling function to assign discrete objects to regular grids for fast Fourier transform are proposed to clean alias effects.Numerical experiments prove that the implementation can achieve sub-percent precision till close to the Nyquist frequency.The impact of removing bulk flow on the estimation of momentum power spectra is derived theoretically and verified numerically.Subtracting bulk flow has little effects at large scales but might induce meaningful differences in nonlinear regime,and probably it is not necessary to subtract bulk flow for samples which peculiar velocities are exact or sufficiently accurate.Momentum power spectra of dark matter samples from N-body simulation are measured and discussed.As expected,the prediction of the one loop Eulerian perturbation theory agrees with simulation only slightly better than the linear theory at z=0,but can be applied to higher redshift with improved accuracy.Measurements of simulation data and the one loop Eulerian theory both reveal that the momentum field contains strong rotational part,and there is a large stochastic component in the divergence of momentum which is not correlated with the density field.The three kinds of momentum power spectra have their own characteristics.

New Probability Distributions in Astrophysics: V. The Truncated Weibull Distribution

We demonstrate that certain astrophysical distributions can be modelled with the truncated Weibull distribution, which can lead to some insights: in particular, we report the average value, the rth moment, the variance, the median, the mode, the generation of random numbers, and the evaluation of the two parameters with maximum likelihood estimators. The first application of the Weibull distribution is the initial mass function for stars. The magnitude version of the Weibull distribution is applied to the luminosity function for the Sloan Digital Sky Survey (SDSS) galaxies and to the photometric maximum of the 2MASS Redshift Survey (2MRS) galaxies. The truncated Weibull luminosity function allows us to model the average value of the absolute magnitude as a function of the redshift for the 2MRS galaxies.

An optimal method for the power spectrum measurement

An aliasing effect brought up by mass assignment onto Fast Fourier Transformation （FFT） grids may bias measurement of the power spectrum of large scale structures. In this paper, based on the Beylkin＇s unequally spaced FFT technique, we propose a new precise method to extract the true power spectrum of a large discrete data set. We compare the traditional mass assignment schemes with the new method using the Daub6 and the 3rd-order B-spline scaling functions. Our measurement of Poisson samples and samples of N-body simulations shows that the B-spline scaling function is an optimal choice for mass assignment in the sense that （1） it has a compact support in real space and thus yields an efficient algorithm （2） without any extra corrections. The Fourier space behavior of the 3rd-order B-spline scaling function enables it to be able to accurately recover the true power spectrum with errors less than 5% up to k 〈 kN. It is expected that such a method can be applied to higher order statistics in Fourier space and will enable us to have a precision capture of the non-Gaussian features in the large scale structure of the universe.

New Probability Distributions in Astrophysics: VI. The Truncated Sujatha Distribution

The truncated version of the two-parameter Sujatha distribution is analysed. In particular, its probability density function and distribution function are obtained. The results are applied to the initial mass function for stars, to the luminosity function for galaxies, to the number of galaxies as a function of the redshift and to the average absolute magnitude of a galaxy as a function of its redshift.

A brief review on cosmological analysis of galaxy surveys with multiple tracers

Galaxy redshift surveys are one of the key probes in modern cosmology.In the data analysis of galaxy surveys,the precision of the statistical measurement is primarily limited by the cosmic variance on large scales.Fortunately,this limitation can in principle be mitigated by observing multiple types of biased tracers.In this brief review,we present the idea of the multi-tracer method,outline key steps in the data analysis and show several worked examples based on the GAMA,BOSS and e BOSS galaxy surveys.This work is a part of a special issue dedicated to the 20 th anniversary of RAA(2001–2020),which is prefaced in Wang&Ip(2020).

Primordial non-Gaussianity from LAMOST surveys

The primordial non-Gaussianity （PNG） in the matter density perturbation is a very powerful probe of the physics of the very early Universe. The local PNG can induce a distinct scale-dependent bias on the large scale structure distribution of galaxies and quasars, which could be used for constraining it. We study the detection limits of PNG from the surveys of the LAMOST telescope. The cases of the main galaxy survey, the luminous red galaxy （LRG） survey, and the quasar survey of dif- ferent magnitude limits are considered. We find that the Mainl sample （i.e. the main galaxy survey which is one magnitude deeper than the SDSS main galaxy survey, or r 〈 18.8） could only provide a very weak constraint on PNG. For the Main2 sample （r 〈 19.8） and the LRG survey, the 2or （95.5%） limits on the PNG parameter fNL are ｜ fNL｜〈 145 and ｜ fNL｜ 〈 114 respectively, which are comparable to the current limit from cosmic microwave background （CMB） data. The quasar survey could provide a much more stringent constraint, and we find that the 2a limit for ｜fNL｜ is between 50 and 103, depending on the magnitude limit of the survey. With Planck-like priors on cosmological parameters, the quasar survey with g 〈 21.65 would improve the constraint to I fNLI 〈 43 （2or）. We also discuss the possibility of further tightening the constraint by using the relative bias method proposed by Seljak.

A transitioning universe with time varying G and decaying Λ

We present a model of a universe that transitions from an early deceleration phase to the current acceleration phase under the framework of general relativity, in the presence of gravitational coupling G（t） and cosmological terms A（t）. Einstein＇s field equations have been solved by considering the time dependent deceleration parameter （DP） which renders the scale factor e = （thekt）1/m where m, n and k are positive con- stants. The cosmological term （A （t）） is found to be positive and a decreasing function of time, which supports the result obtained from observations of type Ia supernovae. The geometrical and kinematical features of the model are examined in detail.

Probing dynamics of dark energy with latest observations

We examine the validity of the ACDM model and probe the dynamics of dark energy with the latest astronomical observations. Using the Ore（z） diagnosis, we find that various kinds of observational data are in tension within the ACDM framework. We then allow for dynamics of dark energy and investigate the constraint on dark energy parameters. We find that for two different kinds of parametri- sations of the equation of state parameter w, a combination of current data mildly favours an evolving w, although the significance is not sufficient for it to be supported by Bayesian evidence. A forecast of the DESI survey shows that the dynamics of dark energy could be detected at the 7σ confidence level and would be decisively supported by Bayesian evidence, if the best-fit model of w derived from current data is the true model.

Probing the Missing Baryons via kSZ Stacking

Kinetic Sunyaev-Zel＇dovich （kSZ） stacking has great potential to become a powerful probe of missing baryons, due to advances in CMB experiments and galaxy surveys. In this paper, we study kSZ stacking in hydrodynamic simulations with different gastrophysics. We quantify the kSZ stacking signal as a function of halo mass, redshift and projection depth. We compare between different simulations to estimate the impact of gastrophysics such as cooling and supernova feedback. Furthermore, we measure the contribution from warm-hot intergalactic medium （WHIM）, which is believed to be the reservoir for most, if not all, missing baryons. We find that the WHIM contribution is significant, at the level of ~ 10%-70%, depending on the angular separation from the stacked halos and other factors. However, contribution from the intracluster medium along the line of sight is in general non-negligible. This complexity requires more detailed and comprehensive analysis on probing the missing baryons with kSZ stacking.

Low-ionization galaxies and evolution in a pilot survey up to z=1

We present galactic spectroscopic data from a pencil beam of 10.75×7.5 centered on the X-ray cluster RXJ0054.0–2823 at z=0.29.We study the spectral evolution of galaxies from z=1 down to the cluster redshift in a magnitude-limited sample at R≤23,for which the statistical properties of the sample are well understood.We divide emission-line galaxies into star-forming galaxies,Low Ionization Nuclear Emission line Regions（LINERs） ,and Seyferts by using emission-line ratios of[OII],Hβ,and[OIII],and derive stellar fractions from population synthesis models. We focus our analysis on absorption and low-ionization galaxies.For absorption-line galaxies,we recover the well-known result that these galaxies have had no detectable evolution since z～0.6-0.7,but we also find that in the range z=0.65-1,at least 50% of the stars in bright absorption systems are younger than 2.5 Gyr.Faint absorption-line galaxies in the cluster at z=0.29 also had significant star formation during the previous 2-3 Gyr,but their brighter counterparts seem to be only composed of old stars.At z～0.8,our dynamically young cluster had a truncated red-sequence.This result seems to be consistent with a scenario where the final assembly of E/S0 took place at z1.In the volume-limited range 0.35≤z≤0.65,we find that 23% of the early-type galaxies have LINER-like spectra with Hβin absorption and have a significant component of A stars.The vast majority of LINERs in our sample have significant populations of young and intermediate-aged stars and are thus not related to AGNs,but to the population of‘retired galaxies’recently identified by Cid Fernandes et al.in the Sloan Digital Sky Survey（SDSS） .Early-type LINERs with various fractions of A stars and E＋A galaxies appear to play an important role in the formation of the red sequence.

New Probability Distributions in Astrophysics: VIII. The Truncated Weibull—Pareto Distribution

We derive the truncated version of the Weibull—Pareto distribution, deriving the probability density function, the distribution function, the average value, the rth moment about the origin, the media, the random generation of values and the maximum likelihood estimator which allows deriving the three parameters. The astrophysical applications of the Weibull—Pareto distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the luminosity function for QSO and the photometric maximum of galaxies of the 2 MASS Redshift Survey.

Improving constraint onΩ_(m)from SDSS using marked correlation functions

Large-scale structure(LSS)surveys will increasingly provide stringent constraints on our cosmological models.Recently,the density-marked correlation function(MCF)has been introduced,offering an easily computable density-correlation statistic.Simulations have demonstrated that MCFs offer additional,independent constraints on cosmological models beyond the standard two-point correlation(2PCF).In this study,we apply MCFs for the first time to SDSS CMASS data,aiming to investigate the statistical information regarding clustering and anisotropy properties in the Universe and assess the performance of various weighting schemes in MCFs,and finally obtain constraints onΩ_(m).Upon analyzing the CMASS data,we observe that,by combining different weights(α=[-0.2,0,0.2,0.6]),the MCFs provide a tight and independent constraint on the cosmological parameterΩ_(m),yieldingΩ_(m)=0.293±0.006 at the 1σlevel,which represents a significant reduction in the statistical error by a factor of 3.4 compared to that from 2PCF.Our constraint is consistent with recent findings from the small-scale clustering of BOSS galaxies(Zhai et al.Astronphys.J.948,99(2023))within the 1σlevel.However,we also find that our estimate is lower than the Planck measurements by about 2.6σ,indicating the potential presence of new physics beyond the standard cosmological model if all the systematics are fully corrected.The method outlined in this study can be extended to other surveys and datasets,allowing for the constraint of other cosmological parameters.Additionally,it serves as a valuable tool for forthcoming emulator analysis on the Chinese Space Station Telescope(CSST).

Elucidating galaxy assembly bias in SDSS

We investigate the level of galaxy assembly bias in the Sloan Digital Sky Survey (SDSS) main galaxy sample using ELUCID,a state-of-the-art constrained simulation that accurately reconstructed the initial density perturbations within the SDSS volume.On top of the ELUCID haloes,we develop an extended HOD model that includes the assembly bias of central and satellite galaxies,parameterized as Q_(cen)and Q_(sat),respectively,to predict a suite of one-and two-point observables.In particular,our fiducial constraint employs the probability distribution of the galaxy number counts measured on 8 h^(-1)Mpc scales N_8^(g) and the projected cross-correlation functions of quintiles of galaxies selected by N_(8)^(g) with our entire galaxy sample.We perform extensive tests of the efficacy of our method by fitting the same observables to mock data using both constrained and non-constrained simulations.We discover that in many cases the level of cosmic variance between the two simulations can produce biased constraints that lead to an erroneous detection of galaxy assembly bias if the non-constrained simulation is used.When applying our method to the SDSS data,the ELUCID reconstruction effectively removes an otherwise strong degeneracy between cosmic variance and galaxy assembly bias in SDSS,enabling us to derive an accurate and stringent constraint on the latter.Our fiducial ELUCID constraint,for galaxies above a stellar mass threshold M_(*)=10^(10.2)h^(-2)M_(⊙),is Q_(cen)=-0.09±0.05 and Q_(sat)=0.09±0.10,indicating no evidence for a significant (>2σ) galaxy assembly bias in the local Universe probed by SDSS.Finally,our method provides a promising path to the robust modelling of the galaxy-halo connection within future surveys like DESI and PFS.