Showing papers on "Correlation function (statistical mechanics) published in 2009"

Ecological information from spatial patterns of plants: insights from point process theory

Abstract: Summary 1. This article reviews the application of some summary statistics from current theory of spatial point processes for extracting information from spatial patterns of plants. Theoretical measures and issues connected with their estimation are described. Results are illustrated in the context of specific ecological questions about spatial patterns of trees in two forests. 2. The pair correlation function, related to Ripley’s K function, provides a formal measure of the density of neighbouring plants and makes precise the general notion of a ‘plant’s-eye’ view of a community. The pair correlation function can also be used to describe spatial relationships of neighbouring plants with different qualitative properties, such as species identity and size class. 3. The mark correlation function can be used to describe the spatial relationships of quantitative measures (e.g. biomass). We discuss two types of correlation function for quantitative marks. Applying these functions to the distribution of biomass in a temperate forest, it is shown that the spatial pattern of biomass is uncoupled from the spatial pattern of plant locations. 4. The inhomogeneous pair correlation function enables first-order heterogeneity in the environment to be removed from second-order spatial statistics. We illustrate this for a tree species in a forest of high topographic heterogeneity and show that spatial aggregation remains after allowing for spatial variation in density. An alternative method, the master function, takes a weighted average of homogeneous pair correlation functions computed in subareas; when applied to the same data and compared with the former method, the spatial aggregations are smaller in size. 5. Synthesis. These spatial statistics, especially those derived from pair densities, will help ecologists to extract important ecological information from intricate spatially correlated plants in populations and communities.

Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

Abstract: We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin–spin correlation function of the XXZ Heisenberg spin- 1/2 chain (with magnetic field) in the disordered regime as well as to the density–density correlation function of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.

The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

Abstract: We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.

Nonlinear evolution of baryon acoustic oscillations from improved perturbation theory in real and redshift spaces

Abstract: We study the nonlinear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, which provides a nonperturbative way to treat the gravitational clustering of large-scale structure, we apply the closure approximation that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and nonlinear propagator. The resultant integral expressions are basically equivalent to those previously derived in the form of evolution equations, and they keep important nonperturbative properties which can dramatically improve the prediction of nonlinear power spectrum. Employing the Born approximation, we then derive the analytic expressions for nonlinear power spectrum and the predictions are made for nonlinear evolution of baryon acoustic oscillations in power spectrum and correlation function. We find that the improved PT possesses a better convergence property compared with standard PT calculation. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of nonlinear redshift-space distortion, we also evaluate the power spectrummore » and correlation function in redshift space. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with the currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few h{sup -3} Gpc{sup 3} at z > or approx. 0.5.« less

Thermodynamics of bcc metals in phase-field-crystal models

Abstract: We examine the influence of different forms of the free-energy functionals used in the phase-field-crystal (PFC) model, and compare them with the second-order density-functional theory (DFT) of freezing, by using bcc iron as an example case. We show that there are large differences between the PFC and the DFT and it is difficult to obtain reasonable parameters for existing PFC models directly from the DFT. Therefore, we propose a way of expanding the correlation function in terms of gradients that allows us to incorporate the bulk modulus of the liquid as an additional parameter in the theory. We show that this functional reproduces reasonable values for both bulk and surface properties of bcc iron, and therefore it should be useful in modeling bcc materials. As a further demonstration, we also calculate the grain boundary energy as a function of misorientation for a symmetric tilt boundary close to the melting transition.

Ensemble covariances adaptively localized with ECO-RAP. Part 1: tests on simple error models

Abstract: In atmospheric data assimilation (DA), observations over a 6–12-h time window are used to estimate the state. Non-adaptive moderation or localization functions are widely used in ensemble DA to reduce the amplitude of spurious ensemble correlations. These functions are inappropriate (1) if true error correlation functions move a comparable distance to the localization length scale over the time window and/or (2) if the widths of true error correlation functions are highly flow dependent. A method for generating localization functions that move with the true error correlation functions and that also adapt to the width of the true error correlation function is given. The method uses ensemble correlations raised to a power (ECO-RAP). A gallery of periodic one-dimensional error models is used to show how the method uses error propagation information and error correlation width information retained by powers of raw ensemble correlations to propagate and adaptively adjust the width of the localization function. It is found that ECO-RAP localization outperforms non-adaptive localization when the true errors are propagating or the error correlation length scale is varying and is as good as non-adaptive localization when such variations in error covariance structure are absent.

Density ripples in expanding low-dimensional gases as a probe of correlations

Abstract: We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of ``density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.

The gravitational shear-intrinsic ellipticity correlation functions of luminous red galaxies in observation and in the λcdm model

Abstract: We examine whether the gravitational shear-intrinsic ellipticity (GI) correlation function of the luminous red galaxies (LRGs) can be modeled with the distribution function of a misalignment angle advocated recently by Okumura et al. For this purpose, we have accurately measured the GI correlation for the LRGs in the Data Release 6 (DR6) of the Sloan Digital Sky Survey (SDSS), which confirms the results of Hirata et al. who used the DR4 data. By comparing the GI correlation functions in the simulation and in the observation, we find that the GI correlation can be modeled in the current Lambda CDM model if the misalignment follows a Gaussian distribution with a zero mean and a typical misalignment angle sigma(theta) = 34.9(-2.1)(+1.9) degrees. We also find a correlation between the axis ratios and intrinsic alignments of LRGs. This effect should be taken into account in theoretical modeling of the GI and intrinsic ellipticity-ellipticity correlations for weak lensing surveys.

The correlation function of optically selected galaxy clusters in the sloan digital sky survey

Abstract: We measure the two-point spatial correlation function for clusters selected from the photometric MaxBCG galaxy cluster catalog for the Sloan Digital Sky Survey (SDSS). We evaluate the correlation function for several cluster samples using different cuts in cluster richness. Fitting the results to power laws, ?cc(r) = (r/R 0)??, the estimated correlation length R 0 as a function of richness is broadly consistent with previous cluster observations and with expectations from N-body simulations. We study how the linear bias parameter scales with richness and compare our results to theoretical predictions. Since these measurements extend to very large scales, we also compare them to models that include the baryon acoustic oscillation feature and that account for the smoothing effects induced by errors in the cluster photometric redshift estimates. For the largest cluster sample, corresponding to a richness threshold of N 200 ? 10, we find only weak evidence, of about 1.4?-1.7? significance, for the baryonic acoustic oscillation signature in the cluster correlation function.

The fluctuation-dissipation relation: how does one compare correlation functions and responses?

Abstract: We discuss the well known Einstein and the Kubo fluctuation-dissipation relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multivariate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR can be more insightful than a definition of 'non-equilibrium' or 'effective temperatures'.

Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature

Abstract: The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform one-dimensional Bose gas with repulsive contact interactions at finite temperatures. Long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes from ideal gas to strongly interacting and from zero temperature to high temperature (Gross-Pitaevskii) and strongly interacting (Tonks-Girardeau) gases. We present perturbative analytic methods, available at strong and weak couplings, and first-principles numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.

Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

Abstract: We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the dynamical Casimir emission of pairs of Bogoliubov phonons when the atom-atom scattering length is modulated in time. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical calculations of Hawking radiation from analog black holes.

Generation of spike trains with controlled auto-and cross-correlation functions

Abstract: Emerging evidence indicates that information processing, as well as learning and memory processes, in both the network and single-neuron levels are highly dependent on the correlation structure of multiple spike trains. Contemporary experimental as well as theoretical studies that involve quasi-realistic neuronal stimulation thus require a method for controlling spike train correlations. This letter introduces a general new strategy for generating multiple spike trains with exactly controlled mean firing rates and correlation structure (defined in terms of auto-and cross-correlation functions). Our approach nonlinearly transforms random gaussian-distributed processes with a predistorted correlation structure into nonnegative rate processes, which are then used to generate doubly stochastic Poisson point processes with the required correlation structure. We show how this approach can be used to generate stationary or nonstationary spike trains from small or large groups of neurons with diverse auto-and cross-correlation structures. We analyze and derive analytical formulas for the high-order correlation structure of generated spike trains and discuss the limitations of this approach.

Particle mesh simulations of the Lyman-alpha forest and the signature of Baryon Acoustic Oscillations in the intergalactic medium

Abstract: We present a set of ultra-large particle-mesh simulations of the LyA forest targeted at understanding the imprint of baryon acoustic oscillations (BAO) in the inter-galactic medium. We use 9 dark matter only simulations which can, for the first time, simultaneously resolve the Jeans scale of the intergalactic gas while covering the large volumes required to adequately sample the acoustic feature. Mock absorption spectra are generated using the fluctuating Gunn-Peterson approximation which have approximately correct flux probability density functions (PDFs) and small-scale power spectra. On larger scales there is clear evidence in the redshift space correlation function for an acoustic feature, which matches a linear theory template with constant bias. These spectra, which we make publicly available, can be used to test pipelines, plan future experiments and model various physical effects. As an illustration we discuss the basic properties of the acoustic signal in the forest, the scaling of errors with noise and source number density, modified statistics to treat mean flux evolution and misestimation, and non-gravitational sources such as fluctuations in the photo-ionizing background and temperature fluctuations due to HeII reionization.

New relations for correlation functions in Navier-Stokes turbulence

Abstract: We consider the steady-state statistics of turbulence sustained by a large-scale force. The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current-density correlation function. Using that, we derive an analog of the flux relation for compressible turbulence and a new exact relation for incompressible turbulence.

Intricate coupling between ion-ion and ion-surface correlations in double layers as illustrated by charge inversion—combined effects of strong Coulomb correlations and excluded volume

Abstract: Many-body correlations in electrolyte systems are important when the electrostatic coupling and/or the volume fraction of ions are not low. Such correlations are ignored in the traditional theories of electrolytes based on the Poisson-Boltzmann approximation. In the general case, the ion density profiles (ion-surface correlation functions) and the ion-ion correlation functions in diffuse electric double layers are strongly interdependent. Both have to be included in the treatment of the system to capture many essential properties. In this work the coupling between the ion-ion and ion-surface correlations and effects of this coupling are illustrated explicitly and graphically (visually). The average forces that act on the ions in the double layer are analysed. This leads to an understanding of mechanisms in action in the inhomogeneous electrolyte near a surface. Charge separation in an electrolyte outside an uncharged surface and charge inversion of highly charged surfaces are thereby used as examples of what insights can be gained by this kind of approach. Some links to mechanisms behind like-charge attraction are also discussed.

Numerical model of longitudinal wave scattering in polycrystals

Abstract: The scattering of elastic waves in polycrystalline materials is relevant for ultrasonic materials characterization and nondestructive evaluation (NDE). Ultrasonic attenuation is used widely to extract microstructural parameters such as grain size. Accurate interpretation of experimental data requires robust scattering models. Such models typically assume constant density, uniform grain size, and ergodicity hypotheses. The accuracy and limits of applicability of these models cannot be fully tested with experiments due to practical limits of real materials processing. Here, this problem is examined in terms of numerical simulations using Voronoi polycrystals that are discretized using finite elements. Wave propagation is studied by integrating the system directly in time using a planestrain formulation. Voronoi polycrystals with cubic symmetry and random orientations are used making the bulk material statistically isotropic. Example numerical results for materials with various degrees of scattering that are of common interest are presented. The numerical results are presented and compared with scattering theory for a wide range of frequencies. The numerical results show good agreement with the theory for the examples examined with evidence that the correlation function is frequency dependent. These results are anticipated to impact ultrasonic NDE of polycrystalline media.

Statistical characterization of gas-patch distributions in partially saturated rocks

Abstract: Reservoirrocksareoftensaturatedbytwoormorefluidphases forming complex patterns on all length scales. The objective of thisworkistoquantifythegeometryoffluidphasedistributionin partially saturated porous rocks using statistical methods and to modeltheassociatedacousticsignatures.BasedonX-raytomographic images at submillimeter resolution obtained during a gasinjection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Mapsofthecontinuousvariationofthepercentageofgassaturationarecomputedandassociatedbinarymapsobtainedthrougha global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from thebinarygas-distributionmapsusingMonteCarlosimulations. The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity andhencesignificancewithrespecttothepercentageofgassaturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantifyfluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measuresarelinkedtoamodelthatpredictscompressionalwave attenuationanddispersionfromlocal,wave-inducedfluidflowin randomly heterogeneous poroelastic solids. In particular, for a limestone sample, withflow permeability of 5 darcies and an average gas saturation of 5%, significant P-wave attenuation is predictedatultrasonicfrequencies.

Electronic structure, linear, and nonlinear optical responses in magnetoelectric multiferroic material BiFeO(3).

Abstract: BiFeO3 has attracted great interest for its multiferroic property. The spontaneous electric polarization, multiferroism, and static magnetoelectric coupling have been widely studied both experimentally and theoretically. Here, in this paper, we report on the effects of magnetic ordering, spin fluctuation, and external magnetic field on the linear dielectric function and second-harmonic generation (SHG) in multiferroic BiFeO3. First, our generalized gradient approximation plus Hubbard U calculations reproduce very well experimental data of linear dielectric function. In the mean time, it is revealed that SHG susceptibilities differ dramatically between antiferromagnetic configuration and ferromagnetic one, which is due to the enhanced contrast in the double-photon resonance absorption. Further Monte Carlo simulation of the coupling between electric order and spin-pair correlation function is presented for the spin fluctuation dependence of SHG. The significant nonlinear optical magnetoelectric effect aroun...

Global distribution of the decay timescale of mixed layer inertial motions observed by satellite‐tracked drifters

Abstract: [1] The decay timescale of mixed layer inertial amplitudes has been estimated from satellite tracked drifter trajectories from 1990 to 2004 as the e-folding timescale of the temporal correlation functions. The decay timescales increase with latitude in all basins except the North Atlantic. A beta dispersion model shows that dephasing leads to meridional variations of the decay timescale in the North Pacific and the Southern Ocean, but meridional variations of the buoyancy structure in the North Atlantic act to compensate the beta effect, leading to a lack of meridional variation of the decay timescale in that ocean.

General treatment of paramagnetic relaxation enhancement associated with translational diffusion

Abstract: A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al, Mol Phys 48, 329 (1983); Nilsson and Kowalewski, J Magn Reson 146, 345 (2000)] for inner-sphere relaxation It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S=7/2 and S=1, which may correspond to Gd(III) and Ni(II) systems It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slo

A polynomial time computation of the exact correlation structure of k-satisfiability landscapes

Abstract: The autocorrelation function and related correlation length are statistical quantities that capture the ruggedness of the fitness landscape: a measure that is directly related to the hardness of a problem for certain heuristic search algorithms. Typically, these quantities are estimated empirically by sampling along a random walk. In this paper, we show that a polynomial-time Walsh decomposition of the k-satisfiability evaluation function allows us to compute the exact autocorrelation function and correlation length for any given k-satisfiability instance. We also use the decomposition to compute a theoretical expectation for the autocorrelation function and correlation length over the ensemble of instances generated uniformly at random. We find that this expectation is invariant to the constrainedness of the problem as measured by the ratio of clauses to variables. However, we show that filtered problems, which are typically used in local search studies, have a bias that causes a significant deviation from the expected correlation structure of unfiltered, uniformly generated problems.

Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

Abstract: A method is proposed that allows three-dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (μPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.

Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties

Abstract: We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free-particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum, and energy. We eventually specialize to the case of Gaussian wave functions and prove that all basic facts about collapse models, which are known to be true in the white-noise case, hold also in the more general case of non-Markovian dynamics.

Retrieval of Green’s functions of elastic waves from thermal fluctuations of fluid-solid systems

Abstract: Fluctuation-dissipation and flow reversal theorems are used to study long-range correlation of thermal phonons in a stationary heterogeneous mechanical system comprised of arbitrary inhomogeneous fluid flow and anisotropic solid. At thermal equilibrium, with an appropriate choice of physical observables to characterize thermal fluctuations within the fluid and within the solid, the general integral expression for the two-point correlation function of the fluctuations reduces to a linear combination of deterministic Green’s functions, which describe wave propagation in opposite directions between the two points. It is demonstrated that the cross-correlation of thermal noise contains as much information about the environment as can be obtained in active reciprocal transmission experiments with transceivers placed at the two points. These findings suggest a possible application of ambient noise cross-correlation to passive acoustic characterization of inhomogeneous flows in fluid-solid systems in laboratory and geophysical settings.

Density scaling and dynamic correlations in viscous liquids.

Abstract: We use a recently proposed method (Berthier, L.; Biroli, G.; Bouchaud, J.P.; Cipelletti, L.; El Masri, D.; L’Hote, D.; Ladieu, F.; Pierno, M. Science 2005, 310, 1797) to obtain an approximation to the four-point dynamic correlation function from derivatives of the linear dielectric response function. For four liquids over a range of pressures, we find that the number of dynamically correlated molecules, Nc, depends essentially only on the magnitude of the relaxation time, τα, independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant τα and the density scaling property of the relaxation times, and implies that Nc also conforms to the same scaling behavior. For propylene carbonate and salol, Nc becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly noncooperative relaxation.

Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids.

Abstract: A multitime probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular-dynamics simulations for simple glass-forming liquids are performed and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics tauhetero is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics tauhetero becomes larger than the alpha-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale tauhetero and the length scale xi of dynamical heterogeneity as tauhetero approximately xiz with z=3.

Structure of correlation functions in single-field inflation

Abstract: Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical That is, if the n-point function is proportional to the (n-1) power of the two-point function amplitude and the fluctuations are small, the probability distribution can be approximated by expanding around a Gaussian in moments However, single-field inflation with higher derivative interactions has a second small number, the sound speed, that appears in the problem when non-Gaussianity is significant and changes the scaling of correlation functions Here we examine the structure of correlation functions in the most general single scalar field action with higher derivatives, formalizing the conditions under which the fluctuations can be expanded around a Gaussian distribution We comment about the special case of the Dirac-Born-Infeld action

Dependence of ridge formation on trigger azimuth: Correlated emission model

Abstract: Ridge formation in near-side correlation in heavy-ion collisions is studied in the framework of a phenomenological model called the correlated emission model. Successive soft emissions due to jet-medium interaction lead to the enhancement of thermal partons that follow the local flow directions. The correlation between the flow direction and the semihard parton direction is the major factor that causes the ridge formation to depend on the trigger direction relative to the reaction plane. With the use of a few parameters we have been able to reproduce the data on the ridge yields as functions of the trigger azimuthal angle for different centralities. An inside-outside asymmetry function is proposed to further probe the characteristics of the azimuthal correlation function. Insights are provided for the understanding of some detailed aspects of the centrality dependence.

A Family of $m$ -Sequences With Five-Valued Cross Correlation

Abstract: Finding the cross correlation between two m-sequences {st} and {sdt} of the same period 2m -1 , that differ by a decimation d, has been a popular research problem since the 1960s. Many cases with three- and four-valued correlation have been determined. Several values of d are known to lead to five-valued cross correlation but their exact correlation distribution has been open. The correlation distribution is completely determined for one of these families with five-valued cross correlation by using evaluations of certain exponential sums including Kloosterman sums. The decimation considered is the special decimation d = 22k+1/2k+1where m is odd and k=1, i.e., d=5/3 . The paper introduces some techniques that may be useful to obtain further results on related decimations.