Shape Of Correlation Function Research Articles

Polynomial Fitting-Based Noise Reduction for Correlation Functions in Medium-Frequency Radar

In the theoretical calculation of atmospheric wind fields using the cross-correlation analysis method of Medium-Frequency radar, it is necessary to compute a series of correlation parameters from the received echo signals, such as autocorrelation and cross-correlation functions, within the main lobe range of the antenna array to retrieve atmospheric parameters. However, both theoretical analysis and practical applications have shown that the shape of correlation functions can be affected by atmospheric conditions and receiver noise, leading to significant biases in the estimated correlation parameters within the main lobe range. In this study, we theoretically analyze the influence of noise on the amplitude of autocorrelation and cross-correlation functions. We propose a noise reduction method based on the characteristics of correlation functions at the zero-delay point to calculate the noise factor and process the correlation functions within the main lobe range. Furthermore, we conduct simulation analysis to evaluate the performance of this noise reduction method and summarize the effects of the number of fitting points and fitting methods on the noise reduction performance.

Chemical potential (in)dependence of hadron scatterings in the hadronic phase of QCD-like theories and its applications

We formulate a method for calculating the hadron-hadron scattering amplitudes at nonzero chemical potential (μ) in the hadronic phase at zero temperature, where the baryon number symmetry remains to be violated. Although it is widely believed that the physical quantities do not change even if we turn on a small μ at zero temperature, the shape of correlation functions for a single hadron depends on μ. Then, the dispersion relation of the single hadron is modified to E(p, μ) = p2+m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{{\ extbf{p}}^2+{m}^2} $$\\end{document} – μnO. Here, m and nO denote the hadron mass at μ = 0 and the quantum number, respectively. From this relation, it is possible that the effective mass of the hadron depends on μ. We extend the HAL QCD method at μ = 0 to the case of μ ≠ 0, which allows us to extract the scattering phase shifts via the interaction potential. We have found that the interaction potential can depend on μ only through the effective mass while the scattering phase shifts, obtained by solving the Schrödinger equation with the interaction potential, are independent of μ. We also numerically analyze the S-wave scatterings of two pions with isospin I = 2 and two scalar diquarks within the framework of QC2D at nonzero quark chemical potential. While the lattice is not exactly set to zero temperature, the μ-independence can be observed. Furthermore, we improve the results for the S-wave scatterings of two hadrons obtained above by taking the μ-independence for granted. Thanks to the asymmetric property of the correlation functions for diquarks at μ ≠ 0, we can access a long-τ regime and can reduce the systematic error coming from inelastic contributions.

A novel method for calculating Bose–Einstein correlation functions with Coulomb final-state interaction

Measurements of Bose–Einstein correlations played a crucial role in the discovery and the subsequent detailed exploration of the Quark-Gluon-Plasma (QGP) created in high-energy collisions of heavy nuclei. Such measurements gave rise to femtoscopy, a flourishing sub-field of high-energy physics, and there are important new directions to explore and discoveries to be made in the near future. One of these important current topics is the precise investigation of the shape of the correlation functions utilizing Lévy-stable sources. In this paper, we utilize Lebesgue’s dominated convergence theorem and Fubini’s theorem to present a novel method of calculating the shape of the two-particle correlation functions, including the Coulomb final-state interaction. This method relies on an exact calculation of a large part of the necessary integrals of the Coulomb wave function and can be utilized to calculate the correlation function for any source function with an easily accessible Fourier transform. In this way, it is eminently applicable to Lévy-stable source functions. In this particular case, we find that the new method is more robust and allows the investigation of a wider parameter range than the previously utilized techniques. We present an easily applicable software package that is ready to use in experimental studies.

Temporal evolution characteristics and prediction methods of spatial correlation function shape of rough soil surfaces

Soil surface roughness is an important boundary parameter that affects land-atmosphere interactions. Previous studies have primarily characterized the temporal-spatial variability of surface roughness parameters based on root mean square height (rmsh) and correlation length (cl), but ignored the change in correlation function shape of rough soil surfaces. In this study, three rough surfaces with different initial roughness (Rough, Medium, and Small) were designed and the temporal changes in their surface heights were observed from 29 April 2015 to 25 August 2015. Through analyzing the temporal variation of the correlation function shape and its prediction methods, the following conclusions were achieved: 1) the fractal correlation function was more consistent with the experimental data than the exponential and Gaussian function; 2) the α value of fractal correlation function represents the correlation function shape, and it changed from 1 (exponential surface) to 2 (Gaussian surface) from the beginning to the end of the experiment; 3) the α prediction method based on Day of Year (DoY) and cumulative rainfall (CR) was better than the rmsh-based method, due to their feasibility for various initial roughness conditions. In general, this study confirmed that correlation function shape of rough soil surfaces is time-dynamic, and we proposed a method for quantifying its temporal dynamics using DoY or CR with the R2 of 0.71 and 0.74 respectively. The results of this study will help to understand the time-varying characteristics of surface roughness parameters and support future research on agricultural remote sensing and wind erosion.

Multiscale local ordering in the prototypical uniaxial relaxor Sr0.6Ba0.4Nb2O6 single crystal at room temperature

The structure and diffuse scattering in uniaxial relaxor Sr0.6Ba0.4Nb2O6 single crystal have been studied by x-ray diffraction at room temperature. Two different kinds of local ordering with different correlation lengths and different shapes of correlation functions have been revealed. The values of correlation lengths have been determined from analysis of experimental data. These types of orderings are connected with the intrinsic structure of crystal and can promote the appearance of relaxor properties.

Correlation of nonlinear noises from different spans in 100 Gb/s multi-span fiber optic lines

The accumulation of nonlinear noise in multi-span communication lines was investigated by numerical modeling and experimentally for different values of accumulated dispersion at input of each span. One coherent 100G channel was investigated (wavelength 1549.32nm, DWDM channel C35). It has been established that interaction of nonlinear noises from two different spans can be described by a correlation function that depends only on values of input dispersion for these spans. It confirms the idea that the nonlinear noise in a fiber optic line is formed mainly due to signal to signal interaction, and the influence of the signal to noise interaction can be neglected. The shape of correlation function was investigated by numerical modeling and experimentally, and its simple approximation was offered. The nonlinear noise in any multi-span line with arbitrary dispersion plan can be calculated based on the investigated correlation function for two spans. It was shown that in a compensated line the offered theoretical model based on correlation function corresponds well to simpler theoretical model based on superlinear dependence of total noise on number of spans.

Geometry and Space-Time Extent of Pion Emission Region at FCC Energies

The energy dependence is investigated for a wide set of space-time characteristics derived from Bose–Einstein correlations of secondary pion pairs produced in proton-proton and nucleus-nucleus interactions. Analytic functions suggested for smooth approximations of the energy dependence of emission region parameters demonstrate reasonable agreement with all available experimental results for proton-proton collisions while the approximations correspond to most of experimental data for nucleus-nucleus collisions at energies above 5 GeV. Estimations for a wide set of space-time quantities are obtained for energies for the Future Circular Collider (FCC) project based on the smooth approximations. The space particle densities at freeze-out are derived also from estimations for the volume of the emission region and for total multiplicity at FCC energies. Estimations for charged particle density and its critical value allow the possibility of lasing behavior for secondary pions in nucleus-nucleus collisions at FCC energy. The mathematical formalism is presented for study of the peak shape of correlation function for general case of central-symmetrical Lévy–Feldheim distribution.

A new soil roughness parameter for the modelling of radar backscattering over bare soil

The characterisation of soil surface roughness is a key requirement for the correct analysis of radar backscattering behaviour. It is noteworthy that an increase in the number of surface roughness parameters in a model also increases the difficulty with which data can be inverted for the purposes of estimating soil parameters. In this paper, a new description of soil surface roughness is proposed for microwave applications. This is based on an original roughness parameter, Zg, which combines the three most commonly used soil parameters: root mean surface height, correlation length, and correlation function shape, into just one parameter. Numerical modelling, based on the moment method and integral equations, is used to evaluate the relevance of this approach. It is applied over a broad dataset of numerically generated surfaces characterised by a large range of surface roughness parameters. A strong correlation is observed between this new parameter and the radar backscattering simulations, for the HH and VV polarisations in the C and X bands. It is proposed to validate this approach using data acquired in the C and X bands, at several agricultural sites in France. It was found that the parameter Zg has a high potential for the analysis of surface roughness using radar measurements. An empirical model is proposed for the simulation of backscattered radar signals over bare soil.

Scale-dependent bias in the baryonic-acoustic-oscillation-scale intergalactic neutral hydrogen

I discuss fluctuations in the neutral hydrogen (HI) density of the z~2.3 intergalactic medium and show that their relation to cosmic overdensity is strongly scale-dependent. This behaviour arises from a linearized version of the well-known "proximity effect", in which bright sources suppress atomic hydrogen density. Using a novel, systematic and detailed linear-theory radiative transfer calculation, I demonstrate how HI density consequently anti-correlates with total matter density when averaged on scales exceeding the Lyman-limit mean-free-path. The radiative transfer thumbprint is highly distinctive and should be measurable in the Lyman-alpha forest. Effects extend to sufficiently small scales to generate significant distortion of the correlation function shape around the baryon acoustic oscillation peak, although the peak location shifts only by 1.2 percent for a mean source bias of b_j=3. The distortion changes significantly with b_j and other astrophysical parameters; measuring it should provide a helpful observational constraint on the nature of ionizing photon sources in the near future.

Cosmological constraints from baryon acoustic oscillations and clustering of large-scale structure

We constrain cosmological parameters using combined measurements of the baryon acoustic oscillation (BAO) feature in the correlation function of galaxies and Ly-\alpha absorbers that together cover 0.1 < z < 2.4. The BAO position measurements alone -- without fixing the absolute sound horizon `standard ruler' length with cosmic microwave background (CMB) data -- constrain \Omega_m = 0.303 +/- 0.040 (68 per cent confidence) for a flat \Lambda CDM model, and w = -1.06^{+0.33}_{-0.32}, \Omega_m = 0.292^{+0.045}_{-0.040} for a flat wCDM model. Adding other large-scale structure (LSS) clustering constraints -- correlation function shape, the Alcock-Paczynski test and growth rate information -- to the BAO considerably tightens constraints (\Omega_m = 0.290 +/- 0.019, H_0 = 67.5 +/- 2.8 km s^{-1} Mpc^{-1}, \sigma_8 = 0.80 +/- 0.05 for \Lambda CDM, and w = -1.14 +/- 0.19 for wCDM). The LSS data mildly prefer a lower value of H_0, and a higher value of \Omega_m, than local distance ladder and type IA supernovae (SNe) measurements, respectively. While tension in the combined CMB, SNe and distance ladder data appears to be relieved by allowing w < -1, this freedom introduces tension with the LSS \sigma_8 constraint from the growth rate of matter fluctuations. The combined constraint on w from CMB, BAO and LSS clustering for a flat wCDM model is w = -1.03 +/- 0.06.

Particle-particle correlation functions as an experimental probe of the nuclear asymmetry energy

The shapes of correlation functions are known to give information about the spatial and temporal extent of an emitting source. Since these two properties can be sensitive to the density-dependence of the asymmetry energy, these functions have been constructed using transport models in the past. In this work, correlation functions extracted using Constrained Molecular Dynamics (CoMD) are used to investigate the possibility of experimentally probing the density-dependence of the asymmetry energy using these correlation functions and detectors with high angular resolution.

Why do stars form in clusters? An analytic model for stellar correlation functions

Recently, we have shown that if the ISM is governed by super-sonic turbulent flows, the excursion-set formalism can be used to calculate the statistics of self-gravitating objects over a wide range of scales. On the largest self-gravitating scales ('first crossing'), these correspond to GMCs, and on the smallest non-fragmenting self-gravitating scales ('last crossing'), to protostellar cores. Here, we extend this formalism to rigorously calculate the auto and cross-correlation functions of cores (and by extension, young stars) as a function of spatial separation and mass, in analogy to the cosmological calculation of halo clustering. We show that this generically predicts that star formation is very strongly clustered on small scales: stars form in clusters, themselves inside GMCs. Outside the binary-star regime, the projected correlation function declines as a weak power-law, until a characteristic scale which corresponds to the characteristic mass scale of GMCs. On much larger scales the clustering declines such that star formation is not strongly biased on galactic scales, relative to the actual dense gas distribution. The precise correlation function shape depends on properties of the turbulent spectrum, but its qualitative behavior is quite general. The predictions agree well with observations of young star and core autocorrelation functions over ~4 dex in radius. Clustered star formation is a generic consequence of supersonic turbulence if most of the power in the velocity field, hence the contribution to density fluctuations, comes from large scales. The distribution of self-gravitating masses near the sonic length is then imprinted by fluctuations on larger scales. We similarly show that the fraction of stars formed in 'isolated' modes should be small (\lesssim10%).

Taming the model zoo: a unified view on correlations in recurrent networks

The meaning of correlated neural activity for the processing and representation of information in cortical networks is still not understood, but evidence for a pivotal role of correlations increases [1]. Recent theoretical work has shown [2-4] that balanced recurrent networks of binary model neurons [3] and spiking integrate-and-fire models [2-4] are able to produce weak correlations despite common input to pairs of cells. For binary model neurons, the theory of correlations in recurrent networks is well established [5]. Investigating learning in recurrent networks with spike-timing dependent plasticity requires spiking neuron models. Theoretical work often employs linear stochastic point process models [6] for their analytic tractability [7]. The diversity of neuron models used in contemporary theoretical neuroscience brings up the question, which features of correlations are generic properties of recurrent networks and which are peculiarities of the often abstracted neuronal dynamics. Moreover, the variety of different theories employed to describe pairwise correlations in neural networks is confusing at times, even for experts in the field. Currently it is unclear how different neuron models relate to each other and whether and how results obtained with one model carry over to another. In this work we present a unified theoretical view on pairwise correlations in recurrent random networks. We consider binary neuron models, leaky integrate-and-fire models, and linear point process models. For networks in the asynchronous irregular regime, we show that these models can be mapped to either of two definitions of an Ornstein-Uhlenbeck (OU) process [8]. The distinction between both classes is how the effective noise enters the model: Leaky integrate-and-fire models and spiking point process models belong to the class with noise on the output side, the binary neuron model is equivalent to an OU process with noise on the input side. The closed solution for the correlation structure of OU processes [8] holds for both classes. We extend this solution to the presence of synaptic conduction delays. The presented theory recovers and unifies the theories of correlations for binary neurons [5] and linear point processes [7] and generalizes both models to the case of finite conduction delays. Moreover we obtain a good approximation for the temporal structure of correlations for the spiking leaky integrate-and-fire model in the asynchronous regime [9]. Finally we show that the oscillatory instability known for networks of integrate-and-fire models [9] is a model-invariant feature of any of the studied dynamics and we explain the class dependent differences in the temporal shape of correlation functions.

In vivo measurement of the shape of the tissue-refractive-index correlation function and its applicationto detection of colorectal field carcinogenesis

Polarization-gated spectroscopy is an established method to depth-selectively interrogate the structural properties of biological tissue. We employ this method in vivo in the azoxymethane (AOM)-treated rat model to monitor the morphological changes that occur in the field of a tumor during early carcinogenesis. The results demonstrate a statistically significant change in the shape of the refractive-index correlation function for AOM-treated rats versus saline-treated controls. Since refractive index is linearly proportional to mass density, these refractive-index changes can be directly linked to alterations in the spatial distribution patterns of macromolecular density. Furthermore, we found that alterations in the shape of the refractive-index correlation function shape were an indicator of both present and future risk of tumor development. These results suggest that noninvasive measurement of the shape of the refractive-index correlation function could be a promising marker of early cancer development.

Analysis of the structure of vibration signals from mechanical systems in the process of growth of a defect

We construct a statistical model of vibration response of a thin body containing a crack and study the dynamics of changes in the cross-correlation links between the stationary components of the vibration signal. It is shown that the crack size affects neither the shape of correlation functions nor the width of their central maximum.

Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering

We apply a new model for the spherically averaged correlation function at large pair separations to the measurement of the clustering of luminous red galaxies (LRGs) made from the SDSS by Cabre and Gaztanaga(2009). Our model takes into account the form of the BAO peak and the large scale shape of the correlation function. We perform a Monte Carlo Markov chain analysis for different combinations of datasets and for different parameter sets. When used in combination with a compilation of the latest CMB measurements, the LRG clustering and the latest supernovae results give constraints on cosmological parameters which are comparable and in remarkably good agreement, resolving the tension reported in some studies. The best fitting model in the context of a flat, Lambda-CDM cosmology is specified by Omega_m=0.261+-0.013, Omega_b=0.044+-0.001, n_s=0.96+-0.01, H_0=71.6+-1.2 km/s/Mpc and sigma_8=0.80+-0.02. If we allow the time-independent dark energy equation of state parameter to vary, we find results consistent with a cosmological constant at the 5% level using all data sets: w_DE=-0.97+-0.05. The large scale structure measurements by themselves can constrain the dark energy equation of state parameter to w_DE=-1.05+-0.15, independently of CMB or supernovae data. We do not find convincing evidence for an evolving equation of state. We provide a set of "extended distance priors" that contain the most relevant information from the CMB power spectrum and the shape of the LRG correlation function which can be used to constrain dark energy models and spatial curvature. Our model should provide an accurate description of the clustering even in much larger, forthcoming surveys, such as those planned with NASA's JDEM or ESA's Euclid mission.

Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.

Semi-empirical calibration of the IEM backscattering model using radar images and moisture and roughness field measurements

Estimating surface parameters by radar-image inversion requires the use of well-calibrated backscattering models. None of the existing models is capable of correctly simulating scatterometer or satellite radar data. We propose a semi-empirical calibration of the Integral Equation Model (IEM) backscattering model in order to better reproduce the radar backscattering coefficient over bare agricultural soils. As correlation length is not only the least accurate but also the most difficult to measure of the parameters required in the models, we propose that it be replaced by a calibration parameter that would be estimated empirically from experimental databases of radar images and field measurements. This calibration was carried out using a number of radar configurations with different incidence angles, polarization configurations, and radar frequencies. Using several databases, the relationship between the calibration parameter and the surface roughness was determined for each radar configuration. In addition, the effect of the correlation function shape on IEM performance was studied using the three correlation functions (exponential, fractal, and Gaussian). The calibrated version of the IEM was then validated using another independent set of experimental data. The results show good agreement between the backscattering coefficient provided by the radar systems and that simulated by the calibrated version of the IEM. This calibrated version of the IEM can be used in inversion procedures to retrieve surface roughness and/or moisture values from radar images.

Lineshapes of dynamical correlation functions in Heisenberg chains

We calculate line shapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal field theory, density of states, and Bethe ansatz. The numerical data have different finite size accuracy in case of the imaginary and real parts in the frequency and time representations of spin-correlation functions, respectively. The low temperature, conformally invariant regime crosses over at $T^*\approx 0.7J$ to a diffusive regime that in turn connects continuously to the high temperature, interacting fermion regime. The first moment sum rule is determined.

Polystyrene local dynamics in dilute solution: Temperature and solvent dependence of C-D vector correlation function shape

Variable temperature 2H-NMR T 1 experiments were performed on backbone deuterated atactic polystyrene in four solvents at two Larmor frequencies. Temperature-frequency superposition, which is consistent with experimental results for many other polymers, cannot describe our data. This indicates that the shape of the correlation function for C-D vector reorientation is temperature dependent. A modified log X 2 distribution of relaxation times, i.e., a delta function plus a log X 2 distribution, was used to fit the experimental data. These fits are consistent with literature 13 C T 1 and NOE data. As polystyrene local dynamics slow down by a factor of 5, the FWHM of the log X 2 distribution increases from 0.8 to 1.1 decades. Solvent identity does not play a major role in determining the shape of the correlation function. The fraction of the correlation function decay caused by librational motion was determined to be 0.28. The quantity was compared for series of polymers and found to correlate with the size of the side group.