Linear Fluctuations Research Articles

Diet variation in a critically endangered marine predator revealed with stable isotope analysis.

Understanding the foraging ecology of animals gives insights into their trophic relationships and habitat use. We used stable isotope analysis to understand the foraging ecology of a critically endangered marine predator, the Māui dolphin. We analysed carbon and nitrogen isotope ratios of skin samples (n = 101) collected from 1993 to 2021 to investigate temporal changes in diet and niche space. Genetic monitoring associated each sample with a DNA profile which allowed us to assess individual and population level changes in diet. Potential prey and trophic level indicator samples were also collected (n = 166; 15 species) and incorporated in Bayesian mixing models to estimate importance of prey types to Māui dolphin diet. We found isotopic niche space had decreased over time, particularly since the 2008 implementation of a Marine Mammal Sanctuary. We observed a decreasing trend in ∂13C and ∂15N values, but this was not linear and several fluctuations in isotope values occurred over time. The largest variation in isotope values occurred during an El Niño event, suggesting that prey is influenced by climate-driven oceanographic variables. Mixing models indicated relative importance of prey remained constant since 2008. The isotopic variability observed here is not consistent with individual specialization, rather it occurs at the population level.

Dynamical analog spacetimes in nonrelativistic flows

Analogue gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analogue spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic non-relativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we reveal that there exists a dynamical acoustic spacetime on which fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime is shown to have a well defined causal structure and curvature. In addition, we find a classical fluctuation relation for the acoustic horizon of the spacetime that admit scenarios wherein the horizon can grow as well as recede, with the latter being a result with no known analogue in black holes. As an example, we numerically investigate the Bondi flow accreting solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates and changes to a new stable size at late times. In particular, the case of a receding acoustic horizon is realized through `low frequency' perturbations. We discuss our results in the context of more general analogue models and its potential implications on astrophysical accretion flows.

Evolution mapping: a new approach to describe matter clustering in the non-linear regime

ABSTRACT We present a new approach to describe statistics of the non-linear matter density field that exploits a degeneracy in the impact of different cosmological parameters on the linear dimensionless matter power spectrum, $\Delta ^2_{\rm L}(k)$. We classify all cosmological parameters into two groups, shape parameters, which determine the shape of $\Delta ^2_{\rm L}(k)$, and evolution parameters, which only affect its amplitude at any given redshift. With this definition, the time evolution of $\Delta ^2_{\rm L}(k)$ in models with identical shape parameters but different evolution parameters can be mapped from one to the other by relabelling the redshifts that correspond to the same clustering amplitude, which we characterize by the linear mass fluctuation in spheres of radius $12\, {\rm Mpc}$, σ12(z). We use N-body simulations to show that the same evolution-mapping relation gives a good description of the non-linear power spectrum, the halo mass function, or the full density field. The deviations from the exact degeneracy are the result of the different structure formation histories experienced by each model to reach the same clustering amplitude and can be accurately described in terms of differences in the suppression factor g(a) = D(a)/a. These relations can be used to drastically reduce the number of parameters required to describe the cosmology dependence of the power spectrum. We show how this can help to speed up the inference of parameter constraints from cosmological observations. We also present a new design of an emulator of the non-linear power spectrum whose predictions can be adapted to an arbitrary choice of evolution parameters and redshift.

Gyrokinetic analysis of an argon-seeded EDA H-mode in ASDEX Upgrade

Understanding edge-localised-mode (ELM)-free high-confinement (H-)mode scenarios is vital for developing practical future demonstration reactor scenarios. An argon-seeded EDA H-mode discharge performed in ASDEX Upgrade is computationally studied in detail for the first time with the gyrokinetic GENE code using experimental profiles and magnetic equilibrium as direct code inputs. Linear scans outline dominant instabilities in the regime and reveal distinct ion- and electron-scale wavenumber growth-rate peaks for two local core and two local pedestal top scenarios. Linear ion-scale growth rates are found to be relatively insensitive to the addition of argon, and collisionality scans demonstrate increased sensitivity in the pedestal top. The addition of an argon impurity profile while keeping the input main ion temperature gradient (ITG) largely unchanged is found to reduce ITG-driven turbulence in the outer core. Nonlinear electromagnetic simulations reveal close agreement with experimentally predicted heat fluxes in the core, outline key sensitivities to electron $\beta$ and background $\boldsymbol{E\times B}$ shearing, and reveal gyrokinetic challenges in analysing the quasicoherent mode. Global electrostatic nonlinear simulations reduce local simulated heat transport overpredictions at the pedestal top. A quasilinear analysis finds that there is good core agreement but poor agreement in the pedestal between linear and nonlinear temperature and density fluctuation cross-phases. Local simulation limitations are elucidated and paths forward for future computation are suggested.

Linear Nash-Greene fluctuations on the evolution of S_8 and H_0 tensions

We present the perturbation equations in an embedded four space-time from the linear Nash-Greene fluctuations of background metric. In the context of a five-dimensional bulk, we show that the cosmological perturbations are only propagated by the gravitational tensorial field equation. In Newtonian conformal gauge, we study the matter density evolution in sub-horizon regime and on how such scale may be affected by the extrinsic curvature. We apply a joint likelihood analysis to the data by means of the Markov Chain Monte Carlo (MCMC) method for parameter estimation using a pack of recent datasets as the Pantheon Supernovae type Ia, the Baryon Acoustic Oscillations (BAO) from DR12 galaxy sample and Dark Energy Survey (DESY1). We discuss the tensions on the Hubble constant H_0 and the growth amplitude factor S_8 of the observations from Planck 2018 Cosmic Microwave Background (CMB) and the local measurements of H_0 with Hubble Space Telescope (HST) photometry and Gaia EDR3. As a result, we obtain an alleviation below sim 1sigma in the contours (S_8-varOmega _m) at 68.4% confidence level (CL) when compared with DESY1 data. On the other hand, the H_0 tension persists with sim 2.6sigma at 68.4% CL and 1.95sigma at 95.7% CL, aggravated with the inclusion of BAO data.

Vacuum decay induced by quantum fluctuations

We treat the effects of quantum field fluctuations on the decay of a meta-stable state of a self-coupled scalar field. We consider two varieties of field fluctuations and their potential effects in a semiclassical description. The first are the fluctuations of the time derivative a free massive scalar field operator, which has been averaged over finite regions of space and time. These fluctuations obey a Gaussian probability distribution. A sufficiently large fluctuation is assumed to produce an effect analogous to a classical initial field velocity, which can cause a finite region to fly over the barrier separating the meta-stable state from the stable vacuum state. Here we find a contribution to the decay rate which is comparable to the decay rate by quantum tunneling, as computed in an instanton approximation. This result is consistent with those of other authors. We next consider the effects of the fluctuations of operators which are quadratic in the time derivative of the free scalar field. The quadratic operator is also averaged over finite regions of space and of time. Now the probability distribution for the averaged operator falls more slowly than an exponential function, allowing for the possibility of very large fluctuations. We find a contribution to the decay rate which is much larger than those coming from either quantum tunneling or linear field fluctuations, and hence appears to be the dominant decay mechanism.

Approximating Density Probability Distribution Functions Across Cosmologies

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: n s , the spectral slope, and σ L , the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, . We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

Non-perturbative gauge invariant scalar fluctuations of the metric in Higgs inflation from complex geometrical scalar–tensor theory of gravity

In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar–tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index n s and the scalar to tensor ratio r that fit well with the Planck 2018 results. Besides we show that in this model the trans-planckian problem can be avoided.

Non-universality of the mass function: dependence on the growth rate and power spectrum shape

ABSTRACT The abundance of dark matter haloes is one of the key probes of the growth of structure and expansion history of the Universe. Theoretical predictions for this quantity usually assume that, when expressed in a certain form, it depends only on the mass variance of the linear density field. However, cosmological simulations have revealed that this assumption breaks, leading to 10–20 per cent systematic effects. In this paper, we employ a specially designed suite of simulations to further investigate this problem. Specifically, we carry out cosmological N-body simulations where we systematically vary growth history at a fixed linear density field, or vary the power spectrum shape at a fixed growth history. We show that the halo mass function generically depends on these quantities, thus showing a clear signal of non-universality. Most of this effect can be traced back to the way in which the same linear fluctuation grows differently into the non-linear regime depending on details of its assembly history. With these results, we propose a parameterization with explicit dependence on the linear growth rate and power spectrum shape. Using an independent suite of simulations, we show that this fitting function accurately captures the mass function of haloes over cosmologies spanning a vast parameter space, including massive neutrinos and dynamical dark energy. Finally, we employ this tool to improve the accuracy of so-called cosmology-rescaling methods and show they can deliver 2 per cent accurate predictions for the halo mass function over the whole range of currently viable cosmologies.

Time since hemorrhages of traumatic and non-traumatic genesis into the substance of the human brain formation using distribution of linear dichroism fluctuations reconstruction

For a forensic expert-practitioner, it is especially important to objectively diagnose and time since the formation of hemorrhage (TSFH) in the substance of the human brain (SHB) of traumatic and non-traumatic origin, as there are cases when the external examination of the corpse at the scene are absent, and at internal research find hemorrhages in a brain. In forensic practice, to verify the cause of death, physical-optical methods are successfully used, which are based on laser irradiation of biological tissues with subsequent mathematical and statistical processing of the obtained data. Previous studies on the possibility of differentiating the cause of death by traditional polarization methods have yielded positive results, which suggests the possibility of their suitability for verification of the genesis of hemorrhage into the brain. For a forensic expert-practitioner, the main thing is objectivity, accuracy and speed of obtaining the result, which could fully satisfy the methods of laser polarimetry in the case of determining the TSFH of traumatic and non-traumatic origin in SHB. Therefore, it is necessary to continue the development and research of these methods for this purpose.
 Aim of the work. To substantiate the possibility of using the method of differential Mueller-matrix mapping of phase anisotropy to determine the temporal dynamics of maps of linear birefringence of histological sections of human brain in determining the age of hemorrhage in human brain substance and to develop forensic criteria for determining the age. death due to cerebral infarction of ischemic and hemorrhagic origin.
 Materials and methods. To achieve this goal, we studied native histological preparations SHB from 130 corpses with a known time of death. The cause of death was TBI (group II (n=35)), cerebral infarction of ischemic origin (group III (n=32)), hemorrhagic stroke (group IV (n=33)), acute coronary insufficiency (group I – comparison group (n=30)). The values of the distribution of the coordinates of the polarization parameters at the points of the microscopic images at the location of the standard Stokes polarimeter were measured. Experimental measurements of Stokes-parametric images of biological layers were performed according to the method presented in the sources. Subsequently, the obtained data were subjected to statistical processing and evaluation of the obtained results. Statistical moments (SM) of the 1st-4th orders (mean (SM1), variance (SM2), asymmetry (SM3) and excess (SM4)) of each map were determined.
 Results and discussion. Comparative analysis of polarization Mueller-matrix mapping images of SHB sections from all groups revealed the destruction of the polycrystalline structure formed by optically active protein complexes of the brain substance, which indicates a decrease in absolute values and range of their scatter with increasing hemorrhage time. This is indicated by the coordinate inhomogeneity of the Mueller-matrix invariant maps of histological sections of SHB of all groups. For histograms that characterize the distributions of the Mueller-matrix invariant samples from all (comparison groups 1 and experimental 2-4) groups, are characterized by individual and significant variations in the values of statistical moments. Due to this, with increasing hemorrhage time, the value of the mean (SM1) and variance (SM2) decreases. Asymmetry (SM3) and excess (SM4), on the contrary, increase. The analysis of the results of statistical processing of the topographic structure of LD tomograms of fibrillar networks of histological sections of SHB dead from all groups shows a greater temporal dynamics of necrotic destruction of nervous tissue. Accordingly, there is a faster time decrease in the absolute values and the range of scatter of the LD value with increasing TSFH. That is, the diagnostic sensitivity of the statistical moments of the 3rd and 4th orders for azimuthal-invariant Mueller-matrix differentiation of nerve tissue samples of the brain of the deceased of control group 1 and all experimental groups 2-4 (p<0,05) was revealed.
 Conclusions. A series of studies of the effectiveness of a new in forensic practice method of differential Mueller-matrix mapping of partially depolarizing histological sections of SHB and tomographic reproduction of optical anisotropy parameters of their polycrystalline structure revealed a high level of accuracy of differentiation and formation of genesis, even under conditions of small geometric thickness of experimental samples. The range of linear change of values of statistical moments of the 1st - 4th orders which characterize distributions of size of LD of fibrillar networks of histologic sections of SHB of the dead from all groups, makes 24 h. In the range of 6-24 hours, the accuracy of determining the TSFH using statistical processing of the topographic structure of LD tomograms of fibrillar networks of histological sections of TSFH is (30±5) minutes.

Hydrodynamics of simple active liquids: the emergence of velocity correlations

We derive the hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the probability density distribution of their positions, velocities, and orientations, while at a mesoscopic level we switch to a coarse-grained description introducing an appropriate set of hydrodynamic fields given by the lower-order moments of the distribution. In addition to the usual density and polarization fields, the hydrodynamics developed in this paper takes into account the velocity and kinetic temperature fields, which are crucial to understanding new aspects of the behavior of active liquids. By imposing a suitable closure of the hydrodynamic moment equations and truncation of the Born–Bogolubov–Green–Kirkwood–Yvon hierarchy, we obtain a closed set of mesoscopic balance equations. At this stage, we focus our interest on the small deviations of the hydrodynamic fields from their averages and apply the methods of the theory of linear hydrodynamic fluctuations. Our treatment sheds light on the peculiar properties of isotropic active liquids and their emergent dynamical collective phenomena, such as the spontaneous alignment of the particle velocities. We predict the existence within the liquid phase of spatial equal-time Ornstein–Zernike-like velocity correlations both for the longitudinal and the transverse modes. At variance with active solids, in active liquids, the correlation length of the transverse velocity fluctuations is sensibly shorter than the length of the longitudinal fluctuations. In particular, the latter depends on the sound speed and increases with the persistence time, while the former displays a weaker dependence on these parameters. Finally, within the same framework, we derive the dynamical structure factors and the intermediate scattering functions and discuss how the velocity ordering persists in time. We find that the velocity decorrelates on a time-scale much longer than the one characteristic of passive fluids.

Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues

Fitting half-integer generalized Laguerre functions to the evolved, real-space dark matter and halo correlation functions provides a simple way to reconstruct their initial shapes. We show that this methodology also works well in a wide variety of realistic, assembly biased, velocity biased and redshift-space distorted mock galaxy catalogs. We use the linear point feature in the monopole of the redshift-space distorted correlation function to quantify the accuracy of our approach. We find that the linear point estimated from the mock galaxy catalogs is insensitive to the details of the biasing scheme at the subpercent level. However, the linear point scale in the nonlinear, biased, and redshift-space distorted field is systematically offset from its scale in the unbiased linear density fluctuation field by more than 1%. In the Laguerre reconstructed correlation function, this is reduced to sub-percent values, so it provides comparable accuracy and precision to methods that reconstruct the full density field before estimating the distance scale. The linear point in the reconstructed density fields provided by these other methods is likewise precise, accurate, and insensitive to galaxy bias. All reconstructions depend on some input parameters, and marginalizing over uncertainties in the input parameters required for reconstruction can degrade both accuracy and precision. The linear point simplifies the marginalization process, enabling more realistic estimates of the precision of the distance scale estimate for negligible additional computational cost. We show this explicitly for Laguerre reconstruction.

Autoregressive Neural Network EURO STOXX 50 Forecasting Model Based on Principal Component Stock Selection

Purpose: The given study looks into forecast accuracy of a traditional ARIMA model while comparing it to Autoregressive Neural Network (AR-NN) model for 984 trading days on EURO STOXX 50 Index.
 Methodology: A hybrid model is constructed by combining ARIMA model and feed-forward neural network model aiming to attain linear and non-linear price fluctuations. The study also incorporates the investigation of component stock prices of the index, that can be selected to improve the predictability of the hybrid model. 
 Findings:The reached ARIMA (1,1,3) model showed higher scores than AR-NN model however integrating selected exogenous stock prices from the index components gave much notable accuracy results. The selected exogenous stocks were extracted after conducting PCA and model scores were compared via MAPE and RMSE.
 Unique contribution to theory, practice and policy: The major contribution of this work is to provide the researcher and fnancial analyst a systematic approach for development of intelligent methodology to forecast stock market. This paper also presents the outlines of proposed work with the aim to enhance the performance of existing techniques. Therefore, Empirical analysis is employed along with a hybrid model based on a feed-forward Neural Network. Lesser error is attained on the test set of Index stock price by comparing the performance of ARIMA and AR-NN while forecasting. Hence, The components of extracted Index stock price like exogenous features are added to make an influence from the AR-NN model.

Press–Schechter primordial black hole mass functions and their observational constraints

ABSTRACT We present a modification of the Press–Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated with the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of supermassive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well-established monochromatic constraints, there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ${\sim}10^2\, \mathrm{M}_\odot$, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO, which are difficult to explain by stellar collapse.

Subluminal electrostatic noise in isotropic space plasmas. General formulas and nonrelativistic thermal limit

The properties of the collective subluminal electrostatic fluctuations in isotropic plasmas are investigated using the covariant kinetic theory of linear fluctuations based on the correct momentum–velocity relation. The covariant theory correctly accounts for the differences in subluminal and superluminal fluctuations in contrast to the non-covariant theory. The general formalism developed here is valid in unmagnetized plasmas and in magnetized plasmas for wavevectors of electrostatic waves parallel to the direction of the uniform magnetic field. Of particular interest are potential differences between the covariant and the non-covariant approach and the consequences of these differences in modifying observational predictions. For thermal particle distributions of protons and electrons with nonrelativistic equal temperatures, the covariant and non-covariant theories yield exactly the same dispersion function and relation for weakly damped electrostatic waves. Also, the quasi-equilibrium wavenumber spectrum of collective thermal electrostatic noise agrees in both theories apart from the important wavenumber restriction |k|>kc=ωp,e/c. While the non-covariant analysis also yields eigenmode fluctuations at small wavenumbers with superluminal phase speeds, the correct covariant analysis indicates that subluminal electrostatic fluctuations are only generated at wavenumbers |k|>kc by spontaneous emission of the plasma particles. As a consequence, the nonrelativistic thermal electrostatic noise wavenumber spectrum is limited to the wavenumber range ωp,e≤|k|≤kmax. Within a linear fluctuation theory, superluminal electrostatic noise cannot be generated.

Gravitational wave spectra from oscillon formation after inflation

We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute both the properties of the emitted gravitational waves as well as the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape of the spectrum and the amplitude of emitted gravitational waves have a universal feature with the peak around the physical wavenumber k/a ∼ m at the inflaton oscillation starting period, irrespective of the exact potential shape. This can be used as a smoking-gun for deducing the existence of a violent preheating phase and possible oscillon formation after inflation. Despite this apparent universality, we also find differences in the shape of the spectrum of emitted gravitational waves between the two families of potentials, leading to discriminating features between them. In particular, all potentials show the emergence of a two-peak structure in the gravitational wave spectrum, arising at the time of oscillon formation. However, potentials that exhibit efficient parametric resonance tend to smear out this structure and by the end of the simulation the two-peak structure is replaced by one broad peak in the GW spectrum. We further compute the number density and properties of the produced oscillons for each potential choice, finding differences in the number density and size distribution of stable oscillons and transient overdensities. We also perform a linear fluctuation analysis and use the corresponding Floquet charts to relate the results of our simulations to the structure of parametric resonance for the various potential types. We find that the growth rate of the scalar perturbations and the associated oscillon formation time are sensitive to the small-field shape of a potential while the macroscopic physical properties of oscillons such as the total number depend on the large-field shape of a potential.

How the Circular and Linear Conformational Fluctuations of Giant DNA Molecules Change with the Viscosity of the Solvent

How the Circular and Linear Conformational Fluctuations of Giant DNA Molecules Change with the Viscosity of the Solvent

Mathematical modeling of the interaction of the main parts of a wheel tractor and the numerical determination of the operator’s seat oscillation

In article is given mathematically modeling of fluctuation, movement and kinematic forward axle, suspension bracket of a skeleton, engine, cabin and seat of the wheel tractor. It is given an analytical type of the equation, the describing vertical fluctuations and longitudinally angular fluctuations of a cabin and the main parts of the tractor. Using this model will be found as far as distances are displaced the main parts of the tractor at vibration. The equations of linear system fluctuation with one degree of freedom of the under cabin damper, which shock-absorber of the tractor, are described.

Study of driving dynamics of modular forestry tillage machine-tractor units in CAE SolidWorks Motion

The issues of simulation studies driving dynamics of wheeled forestry machine-tractor units on the surface with obstacles are considered. The method of simulation modeling in CAD SolidWorks and CAE SolidWorks Motion is used. A simplified 3d-model of the MTZ-82.1 agricultural wheeled tractor was created, preserving all the main geometric and mass-inertia parameters of the moving elements. The tractor model was equipped with front and rear mounted modular forest tillage implements in the transport position. The research was performed on a virtual track with four different types of obstacles similar to those found in forest conditions. In a computer experiment, three different schemes of units were studied and the following parameters were obtained: wheel lift height, lateral displacement of the center of gravity, and linear speed fluctuations. Analysis of the results showed that the 0+1 scheme (rear-mounted single-row harrow) was the most stable. The heaviest scheme 1+2 (front-mounted drum chopper and rear-mounted two-row harrow) also had satisfactory stability. The least stable was a tractor equipped according to the 0+2 scheme (rear-mounted two-row harrow). The virtual experiment allowed us to study the dynamic stability of various forestry units in the transport position and establish the most stable configurations.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2

ABSTRACT We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of 343 708 spectroscopically confirmed quasars between redshift 0.8 < z < 2.2 are used as tracers of the underlying dark matter field. In comparison with DR14 sample, the final sample doubles the number of objects as well as the survey area. In this paper, we present the analysis in configuration space by measuring the two-point correlation function and decomposing it using the Legendre polynomials. For the full-shape analysis of the Legendre multipole moments, we measure the baryon acoustic oscillation (BAO) distance and the growth rate of the cosmic structure. At an effective redshift of zeff = 1.48, we measure the comoving angular diameter distance DM(zeff)/rdrag = 30.66 ± 0.88, the Hubble distance DH(zeff)/rdrag = 13.11 ± 0.52, and the product of the linear growth rate and the rms linear mass fluctuation on scales of $8 \, h^{-1}\, {\rm Mpc}$, fσ8(zeff) = 0.439 ± 0.048. The accuracy of these measurements is confirmed using an extensive set of mock simulations developed for the quasar sample. The uncertainties on the distance and growth rate measurements have been reduced substantially (∼45 and ∼30 per cent) with respect to the DR14 results. We also perform a BAO-only analysis to cross check the robustness of the methodology of the full-shape analysis. Combining our analysis with the Fourier-space analysis, we arrive at $D^{{\bf c}}_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.21 \pm 0.79$, $D^{{\bf c}}_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.23 \pm 0.47$, and $f\sigma _8^{{\bf c}}(z_{\rm eff}) = 0.462 \pm 0.045$.