Triple Correlation Function Research Articles

Correlations in a weakly interacting two-dimensional random flow.

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us to establish the criterion of validity of the perturbation theory for different ratios of viscosity and bottom friction. We find that the corrections to the second moment are anomalously weak in the cases of small bottom friction and small viscosity and relate the weakness to the energy and enstrophy balances. We demonstrate that at small bottom friction the triple correlation function is characterized by universal scaling behavior in some region of lengths. The developed perturbation method was verified and confirmed by direct numerical simulations.

The fault detection of transmitting current encoded by m-sequence using triple-correlation function in helicopter-borne electromagnetic method.

An m-sequence is applied to the helicopter-borne electromagnetic method system for the first time, and there are many problems to be solved, one of which is the detection of the quality of the transmitting current waveform, which directly affects the resource survey results. In this research, we found that the triple-correlation function (TCF) can reveal the bit integrity characteristics of the m-sequence encoded transmitting current. On this basis, this paper proposes to extract the three-dimensional information of the normalized TCF plot by using a peak detection method and, then, proposes to use a dual-threshold method to clarify the detection results. The whole process realizes the fault detection of the transmitting current waveform. We propose a reasonable transmitting current modeling method and conduct 1200 random experiments in 12 groups. The statistics of the experimental results show that when the number of missing bits is 1, 2, 4, and 8, the fault detection accuracy can reach more than 83%. A comparative experiment using the Field Programmable Gate Array. in the laboratory validates the feasibility of the fault detection method. This method is beneficial to improve the quality of detection data and avoid economic losses caused by invalid detection flights.

Investigation of the degree of local structural similarity between the parent-liquid and children-crystal states for a model soft matter system

We investigate the degree of local structural similarity between the parent-liquid and children-crystal states for a model soft-matter system of particles interacting through the harmonic-repulsive pair potential. At different pressures, this simple system crystallizes into several significantly different crystal structures. Therefore, the model is well suited for addressing the question under consideration. In our studies, we carefully analyze the developments of the pair and triple correlation functions for the parent-liquid as the pressure increases. In particular, these considerations allow us to address the similarities in the orientational orderings of the corresponding liquid and solid phases. It is demonstrated that the similarities in the orientational ordering between the two states extend beyond the first and second neighbors. Currently, it is widely accepted that orientational ordering is important for understanding the behaviors of liquids, supercooled liquids, and the development of detailed theories of the crystallization process. Our results suggest that, up to a certain degree, it might be possible to predict the structures of the children-solids from studies of the parent-liquids. Our results raise anew a general question of how much insight into the properties of the liquid-state can be gained from drawing a parallel with the solid-state.

On the triple correlations of fractional parts of

AbstractFor fixed$\alpha \in [0,1]$, consider the set$S_{\alpha ,N}$of dilated squares$\alpha , 4\alpha , 9\alpha , \dots , N^2\alpha \, $modulo$1$. Rudnick and Sarnak conjectured that, for Lebesgue, almost all such$\alpha $the gap-distribution of$S_{\alpha ,N}$is consistent with the Poisson model (in the limit asNtends to infinity). In this paper, we prove a new estimate for the triple correlations associated with this problem, establishing an asymptotic expression for the third moment of the number of elements of$S_{\alpha ,N}$in a random interval of length$L/N$, provided that$L> N^{1/4+\varepsilon }$. The threshold of$\tfrac {1}{4}$is substantially smaller than the threshold of$\tfrac {1}{2}$(which is the threshold that would be given by a naïve discrepancy estimate).Unlike the theory of pair correlations, rather little is known about triple correlations of the dilations$(\alpha a_n \, \text {mod } 1)_{n=1}^{\infty } $for a nonlacunary sequence$(a_n)_{n=1}^{\infty } $of increasing integers. This is partially due to the fact that the second moment of the triple correlation function is difficult to control, and thus standard techniques involving variance bounds are not applicable. We circumvent this impasse by using an argument inspired by works of Rudnick, Sarnak, and Zaharescu, and Heath-Brown, which connects the triple correlation function to some modular counting problems.In Appendix B, we comment on the relationship between discrepancy and correlation functions, answering a question of Steinerberger.

Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function

An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood’s superposition approximation. Detailed considerations of the peaks’ shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system’s dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids’ dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid’s structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

Ultrafast data mining of molecular assemblies in multiplexed high-density super-resolution images

Multicolor single-molecule localization super-resolution microscopy has enabled visualization of ultrafine spatial organizations of molecular assemblies within cells. Despite many efforts, current approaches for distinguishing and quantifying such organizations remain limited, especially when these are contained within densely distributed super-resolution data. In theory, higher-order correlation such as the Triple-Correlation function is capable of obtaining the spatial configuration of individual molecular assemblies masked within seemingly discorded dense distributions. However, due to their enormous computational cost such analyses are impractical, even for high-end computers. Here, we developed a fast algorithm for Triple-Correlation analyses of high-content multiplexed super-resolution data. This algorithm computes the probability density of all geometric configurations formed by every triple-wise single-molecule localization from three different channels, circumventing impractical 4D Fourier Transforms of the entire megapixel image. This algorithm achieves 102-folds enhancement in computational speed, allowing for high-throughput Triple-Correlation analyses and robust quantification of molecular complexes in multiplexed super-resolution microscopy.

On the Construction of Turbulent Transfer Spectral Models Using 3D Numerical Simulation of Taylor–Green Vortex Decay

In the present paper we recall the classical Taylor–Green vortex turbulent decay in terms of isotropic turbulence theory. In particular, we calculate the spectral turbulent kinetic energy transfer $$T(k)$$ and the spectral flux $${{\Pi }_{E}}(k)$$ basing on the longitudinal triple correlation function (the two-point third-order velocity moment). These functions can be also obtained in other way via the generalized Karman–Howarth equation for homogeneous turbulence using integral of triple modes interaction. In both cases, the spectral transfer and the flux appear to be different from the characteristics of isotropic or homogeneous turbulence due to the peculiarities of the problem statement. The results obtained outline the range of obstacles associated with the construction of spectral turbulent models in complex heat and mass transfer problems arising due to periodicity effects, closeness of integral turbulent scales to modeling box size and lack of spectral resolution.

Blind estimation of pseudo‐random codes in periodic long code direct sequence spread spectrum signals

An estimation method of pseudo-random (PN) codes in the periodic long code direct sequence spread spectrum signals using a pair of spreading code and scrambling code [i.e. long scrambling code direct sequence spread spectrum (LSC-DSSS)] is investigated in this study. Via the investigation of properties of triple correlation function (TCF) of m-sequences, the existence of common peaks in the TCFs of different m-sequences is proved, and the corresponding relationship between common peaks and primitive polynomials is further investigated. Four theorems are proposed as supplements of triple correlation theory and a novel estimation algorithm of the PN codes in LSC-DSSS signals is put forward on the basis of the theorems. With certain carrier frequency and chip rate of spreading code, this algorithm first eliminates the influence of information codes through delay-and-multiply operation. Then the TCF of signal is calculated, and the two PN codes in signal are successfully estimated finally by searching and using the common peak coordinates in the TCF. Simulation results show that the proposed algorithm exhibits excellent performance in estimating PN codes in LSC-DSSS signals.

Analyzing Quantum Correlations Made Simple

AbstractThe understanding of correlations in degenerate nonideal many‐particle systems is complex and theoretically challenging. Using the recently proposed permutation blocking path integral Monte Carlo (PB‐PIMC) scheme, which allows for an exact treatment of many‐body correlations, we study the influence of quantum statistics in a confined few‐particle Coulomb (quantum dot) system. As a versatile tool to gain insight into the internal structure of correlated many‐body systems, the application of triple correlation functions is extended to quantum systems. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Estimation of PN Code of DS-CDMA Signals over Frequency selective Fading Channel in presence of Impulsive noise

Spread spectrum signals are widely used for secure communications, as well as for multiple access interference (MAI). They have many interesting properties, including low probability of interception. Indeed, direct sequence spread spectrum systems (DSSSS) use a periodical pseudo-random sequence to modulate the baseband signal before transmission. Interception of DSSS signals is a difficult task due to the hiding of the PN sequence, especially if the accompanied noise is non-Gaussian and the channel is frequency selective. In this paper, a receiver is proposed to intercept asynchronous direct sequence code division multiple access (DS-CDMA) signals received from different users and estimate the PN sequences of each one of them. The signals are assumed to be transmitted over frequency selective fading channel and contaminated with Class-A impulsive noise. The proposed interception receiver is based on Independent Component Analysis (ICA), the pseudo random sequences is estimated from the eigenvector subspace in case of single path. In multipath situations, the estimation is the overlapped form of the pseudo random sequences, a triple correlation function (TCF) is introduced to eliminate the influence of multipath. The performance of proposed receiver is evaluated in terms of the number of correct estimated codes for m-sequence over typical urban channel in presence of impulsive noise. The results show that the interception receiver performs is 100% code estimation at -8dB signal to noise ratio.

Protein-Protein-Protein Interactions in Membranes Measured by Triple Cross-Correlation of Confocal Images

Protein-protein interactions in binary complexes have been measured successfully and quantitatively by fluorescence correlation spectroscopy in solution (Elson, BJ 101, 2855-2870 (2011)) and image correlation spectroscopy on cell surfaces (Kolin and Wiseman, Cell Biochem Biophys 49, 141-164 (2007)). These tools fail, however, to provide information about ternary complexes i.e. about protein-protein-protein interactions. It has been known for some time that higher order moments or correlations contain the relevant information (Palmer and Thompson, BJ 52, 257-270 (1987); Heinze, Jahnz, and Schwille, BJ 86, 506-516 (2004)) but it is only recently that triple correlation functions of ternary complexes have been measured in solution (Ridgeway, Millar, and Williamson, J. Phys Chem B 116, 1908-1919 (2012) and PNAS 109, 13614-13619 (2012)). Our present work shows how complete and quantitative information can be obtained for ternary complexes of membrane proteins from three confocal images from each of three distinctly labeled protein species by employing a combination of image correlation spectroscopy, image cross-correlation spectroscopy, image triple auto-correlation spectroscopy and image triple cross-correlation spectroscopy.

Breakdown of order in a self-organised barrier discharge

In this work, we investigate the transition of a hexagonal patterned self-organised barrier discharge into a stochastic distributed pattern during voltage reduction. The techniques of 2D Fourier transformation and, for the first time, the triple correlation function are used. Introducing measures for the angular and radial order it is possible to observe a supercritical bifurcation scenario for the decaying order. A chronological sequence of an angular and a radial breakdown of the pattern has been revealed. Possible limits of reproducibility and dependence on the frequency of the applied voltage are estimated.

Peculiarities of the correlation functions, X-ray and neutron scattering in BaTiO3

Based on molecular-dynamics (MD) simulations, we have calculated the static and dynamic correlation functions in a BaTiO3 crystal. The static correlation functions have been used to study the peculiarities of diffuse scattering in barium titanate showing the experimentally observed anomalous planes. Based on time-dependent pair correlation functions, we have calculated the phonon spectra of BaTiO3 and studied the central peak of inelastic scattering. The phonon frequencies calculated by the MD method agree well with those obtained previously in the quasi-harmonic approximation. We show that the central peak of inelastic scattering is associated mainly with the soft optic mode and has the same symmetry. The large anisotropy in the displacements of atoms in the soft mode allows the presence of peculiarities in both X-ray scattering and EXAFS spectroscopy to be explained. The characteristic shape of the EXAFS spectra is shown to be explained by the quasi-one-dimensional motion of the oxygen ions in the cubic lattice of BaTiO3. Our calculation of triple correlation functions shows that the titanium atom in the described model oscillates around the cubic cell center. Explaining the experimental data that have caused disagreement about the nature of the phase transition in BaTiO3 using the developed model gives grounds to treat the phase transition in barium titanate as a displacive one.

The Spectroscopic Basis of Fluorescence Triple Correlation Spectroscopy

We have developed fluorescence triple correlation spectroscopy (F3CS) as an extension of the widely used fluorescence microscopy technique fluorescence correlation spectroscopy. F3CS correlates three signals at once and provides additional capabilities for the study of systems with complex stoichiometry, kinetic processes, and irreversible reactions. A general theory of F3CS was developed to describe the interplay of molecular dynamics and microscope optics, leading to an analytical function to predict experimental triple correlations of molecules that freely diffuse through the tight focus of the microscope. Experimental correlations were calculated from raw fluorescence data using triple correlation integrals that extend multiple-tau correlation theory to delay times in two dimensions. The quality of experimental data was improved by tuning specific spectroscopic parameters and employing multiple independent detectors to minimize optoelectronic artifacts. Experiments with the reversible system of freely diffusing 16S rRNA revealed that triple correlation functions contain symmetries predicted from time-reversal arguments. Irreversible systems are shown to break these symmetries, and correlation strategies were developed to detect time-reversal asymmetries in a comprehensive way with respect to two delay times, each spanning many orders of magnitude in time. The correlation strategies, experimental approaches, and theory developed here enable studies of the composition and dynamics of complex systems using F3CS.

Melting scenarios for three-dimensional dusty plasma clusters

The melting transition of finite three-dimensional dust clouds (Yukawa balls) from a solid-like to a liquid-like state is systematically studied with high spatial and temporal resolution of the individual grains by means of stereoscopy. Two different melting scenarios are reported: Melting is induced first by an increase of plasma power, and second by laser-induced heating. The experiments confirm that melting starts with a loss of orientational correlation, followed by a loss of the radial order upon further heating. While the plasma-power melting is driven via the ion wakefield, laser heating provides a more equilibrium scenario. The internal loss of correlations is well captured by the triple correlation function (TCF) which is insensitive to particle exchanges and the rotation of the cluster as a whole. The critical Coulomb coupling parameter for N=35 is determined as Γ(crit)≈570. The experimental findings are in good agreement with thermodynamic Monte Carlo simulations.

Blind Separation of DS-CDMA Signals with ICA Method

The estimation of pseudo noise sequence and information sequence is of great importance in the security of DS-CDMA system, which remains a hot research problem in reconnaissance and supervision of wireless communication. In DS-CDMA system, the pseudo noise sequences of different users are uncorrelated and the information sequences of different users are statistical independent, thus independent component analysis (ICA) could be introduced to separate the DS-CDMA signals with little prior knowledge. In multipath situations, the recovered pseudo noise sequence with ICA is overlapped. For DS-CDMA signals which utilize m-sequence as pseudo noise sequence, the triple correlation function (TCF) is introduced to eliminate the influence of overlap in this paper , which increases the estimation correct ratio greatly. Under the non - cooperative conditions, it is very difficult for the interceptor to aim at the very beginning of the transmitted signal. Certain offset s between the interceptor and the transmitter deteriorate the blind separation method obviously. The relationship between none convergence and the offset is found out and explained from eigen value decomposition. The validity of the proposed method and theory analysis is proved well by the simulation results at last.

An infinity of possible invariants for decaying homogeneous turbulence

The von Kárman–Howarth equation implies an infinity of invariants corresponding to an infinity of different asymptotic behaviours of the double and triple velocity correlation functions at infinite separations. Given an asymptotic behaviour at infinity for which the Birkhoff–Saffman invariant is not infinite, there are either none, or only one or only two finite invariants. If there are two, one of them is the Loitsyansky invariant and the decay of large eddies cannot be self-similar. We examine the consequences of this infinity of invariants on a particular family of exact solutions of the von Kárman–Howarth equation.

Two-point closure method for turbulence with reacting and mixing chemical elements of type A+B→ C

Turbulence with reacting and mixing chemical elements of type A+B→C was investigated by using the two-point closure method, For implementation of this method, two-point correlation functions and two-point triple correlation functions are defined first. Equations describing the turbulence under study that describe the dynamical behaviour are written in terms of two-point correlation functions and two-point triple correlation functions. These describe the dynamical behaviour of two-point double-reactant fluctuation correlation functions. In each of these equations, two-point triple correlation functions appear. Thus, the characteristic difficulty of indeterminacy in turbulence theory is noticed in these equations too. A simple closure hypothesis for two-point triple correlation functions is proposed with a view to overcoming the indeterminacy. This hypothesis enables one to obtain the closed set of equations for double correlation functions, as desired. The resulting equations for double correlation functions provide theoretical information about the turbulence under investigation. Having obtained the closed set of equations for double correlation functions, the relationships for reactants’ eddy diffusivity functions are derived. Also, the reactants’ energy and transfer functions in fluid space are obtained. Having expressed the Karman–Howarth equations for the present investigation in dimensionless form, these are rewritten in terms of energy functions in fluid space. The system of equations for scales of segregation related to reactants A and B is derived. Various length scales involved in this study can be evaluated on integration of these equations, which in turn generates theoretical information about the turbulence under investigation.

Joint Demodulation and Detection of Covert Modulated M-sequence

Abstract:The paper Present a new receiver for detection of covert M.sequence regardless the chipcode sequences and the type of modulation. A Higher Order Statistics (HOS) based onthe Kurtosis of the received signal is used to classify the type of the modulation, and sodecide the modulator. The Triple Correlations Function (TCF) of M. sequence of thedemodulated which differs from sequence to another according to the feedbackconnection is used to decide the generation function g (x) from the peak position of thisM-sequence. This paper is classified into four sections the first section, we introducesome property of modulation and how the (TCF) of the M.sequence generated.Secondly, the digital modulation classification is classified and tabulated usingtheoretical cumulants Statistics C40, C42. The Triple Correlation function (TCF) ofM.sequence is showed in section three. Computer simulation of determination offeedback polynomial y(x) at section four. Finally, the conclusion is presented in at therest of this paper.

Triple correlation of the Riemann zeros

We use the conjecture of Conrey, Farmer and Zirnbauer for averages of ratios of the Riemann zeta function to calculate all the lower order terms of the triple correlation function of the Riemann zeros. A previous approach was suggested in 1996 by Bogomolny and Keating taking inspiration from semi-classical methods. At that point they did not write out the answer explicitly, so we do that here, illustrating that by our method all the lower order terms down to the constant can be calculated rigourously if one assumes the ratios conjecture of Conrey, Farmer and Zirnbauer. Bogomolny and Keating returned to their previous results simultaneously with this current work, and have written out the full expression. The result presented in this paper agrees precisely with their formula, as well as with our numerical computations, which we include here. We also include an alternate proof of the triple correlation of eigenvalues from random U(N) matrices which follows a nearly identical method to that for the Riemann zeros, but is based on the theorem for averages of ratios of characteristic polynomials.