Kinds Of Correlation Functions Research Articles

Unambiguous Sine-phased BOC(kn,n) Signal Acquisition Based on Combined Correlation Functions

Galileo and GPS have been developing their new signals in recent years. Multiplexed Binary Offset Carrier (MBOC) is the final implementation of Galileo E1 and GPS L1C, which is the multiplexing of BOC(1,1) and BOC(6,1). Therefore, it is helpful to satisfy the demand that the new signals must be compatible with GPS BPSK signal. BOC(kn,n) modulation will provide better track performance and higher positioning accuracy. However, the main drawback of the BOC modulated signal is that its autocorrelation has multiple side peaks around the main peak. This paper will focus on a family of signals: sine-phased BOC(kn,n). We are trying to explore a new method to cancel the side peaks of BOC(kn,n) autocorrelation, making use of two kinds of correlation functions. One is the correlation of the incoming signal and the sine-phased BOC(kn,n) modulated spreading code(PRN code multiplied by subcarrier), and the other is the correlation of the incoming signal and the PRN code only. Two kinds of correlation function are separated into several sub-correlations. Sub-correlations have less side peaks which are in different code delays. Corresponding parts of two sub-correlations will be combined to cancel the side peaks separately, and finally the new function without side peaks will be acquired after several correlations added together. Simulation results will be given. It is shown that the proposed method is contributed to the side peaks cancellation for unambiguous sine-phased BOC (kn, n) signal acquisition.

Correlation combination ambiguity removing technology for acquisition of sine-phased BOC(kn,n) signals

Binary Offset Carrier (BOC) has been chosen as one of modulation methods in the future Global Navigation Satellite Systems (GNSS). Even though BOC signals can bring several advantages such as better track performance and higher positioning accuracy, there is a drawback that the autocorrelation functions have multiple side-peaks if BOC modulation is adopted. This characteristic will lead to false acquisition and the tracking loop will be locked in false phase point. The proposed Correlation Combination Ambiguity Removing Technology (CCART) cancelled all the side-peaks of the sine-phased BOC(kn,n) signals completely by making use of two kinds of correlation functions. Two kinds of sub-correlation functions were combined separately and then final correlation function without side-peaks was acquired. The simulation results are given and compared with other techniques. It is shown that acquisition will not be degraded with the increase of k.

The effects of the physical cluster formation on pair-correlation functions for an ionic fluid

A system of two integral equations, which is equivalent to the Ornstein-Zernike equation, results in two kinds of correlation functions which describe the apparent effects of the physical cluster formation on pair-correlation functions. Each pair-correlation function is equivalent to the sum of the two kinds of correlation functions, and the development of physical clusters, which are formed in an ionic fluid owing to the attractive Coulomb force between positive and negative charged particles, allows the dependence of the sum on the distance r between particular pair particles to develop the deviation from the behavior characterized as r-1. Then, their development makes the dependence of the sum on r have a tendency to approach the behavior characterized as r-3/2, and the two kinds of correlation functions aid in describing fractal structures of nonuniform particle distributions in ionic fluids.

Construction of a microscopic model forf-electron systems on the basis of aj−jcoupling scheme

We construct a microscopic model for f-electron systems, composed of f-electron hopping, Coulomb interaction, and crystalline electric field (CEF) terms. In order to clarify the meaning of one f-electron state, here the j-j coupling scheme is considered, since the spin-orbit interaction is generally large in f-electron systems. Thus, the f-electron state at each site is labelled by $\mu$, namely, the z-component of total angular momentum j. By paying due attention to f-orbital symmetry, the hopping amplitudes between f-electron states are expressed using Slater's integrals. The Coulomb interaction terms among the $\mu$-states are written by Slater-Condon or Racah parameters. Finally, the CEF terms are obtained from the table of Hutchings. The constructed Hamiltonian is regarded as an orbital degenerate Hubbard model, since it includes two pseudo-spin and three pseudo-orbital degrees of freedom. For practical purposes, it is further simplified into a couple of two-orbital models by discarding one of the three orbitals. One of those simplified models is here analyzed using the exact diagonalization method to clarify ground-state properties by evaluating several kinds of correlation functions. Especially, the superconducting pair correlation function in orbital degenerate systems is carefully calculated based on the concept of off-diagonal long-range order. We attempt to discuss a possible relation of the present results with experimental observations for recently discovered heavy fermion superconductors CeMIn$_5$ (M=Ir, Co, and Rh), and a comprehensive scenario to understand superconducting and antiferromagnetic tendencies in the so-called ``115'' materials such as CeMIn$_5$, UMGa$_5$, and PuCoGa$_5$ from the microscopic viewpoint.

Semi-analytic approach to understanding the distribution of neutral hydrogen in the Universe

Analytic derivations of the correlation function and the column density distribution for neutral hydrogen in the intergalactic medium (IGM) are presented, assuming that the non-linear baryonic mass density distribution in the IGM is lognormal. This ansatz was used earlier by Bi & Davidsen to perform one-dimensional simulations of lines of sight and analyse the properties of absorption systems. We have taken a completely analytic approach, which allows us to explore a wide region of the parameter space for our model. The analytic results have been compared with observations to constrain various cosmological and IGM parameters, whenever possible. Two kinds of correlation functions are defined: (i) along the line of sight (LOS); and (ii) across the transverse direction. We find that the effects on the LOS correlation owing to changes in cosmology and the slope of the equation of state of the IGM, γ, are of the same order, which means that we cannot constrain both the parameters simultaneously. However, it is possible to constrain γ and its evolution using the observed LOS correlation function at different epochs provided that one knows the background cosmology. We suggest that the constraints on the evolution of γ obtained using the LOS correlation can be used as an independent tool to probe the reionization history of the Universe. From the transverse correlation function, we obtain the excess probability, over random, of finding two neutral hydrogen overdense regions separated by an angle θ. We find that this excess probability is always less than 1 per cent for redshifts greater than 2. Our models also reproduce the observed column density distribution for neutral hydrogen, and the shape of the distribution depends on γ. Our calculations suggest that one can rule out γ>1.6 for z≃2.31 using the column density distribution. However, one cannot rule out higher values of γ at higher redshifts.

Pressure Fluctuation on Casing Wall of Isolated Axial Compressor Rotors at Low Flow Rate

The pressure fluctuations on the casing wall of two axial flow compressor rotors with various tip clearances have been analyzed by the use of two kinds of correlation functions. The behavior of the pressure fluctuation varies depending on tip clearance and blade solidity. In the case of small tip clearance, the nature of disturbances becomes random as the flow rate is reduced to a stall condition. For moderate tip clearance, coherent-structured disturbances appear intermittently at low flow rate. They appear more frequently as the solidity is increased and the flow rate becomes lower. For large tip clearance, the coherent structured disturbances exist even at considerably higher flow rates. Corresponding to these features, there are peculiar patterns in the correlation designated as “phase-locked correlation functions.”

Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds

The problem of the slow viscous flow of a fluid through a random porous medium is considered. The macroscopic Darcy's law, which defines the fluid permeabilityk, is first derived in an ensemble-average formulation using the method of homogenization. The fluid permeability is given explicitly in terms of a random boundary-value problem. General variational principles, different to ones suggested earlier, are then formulated in order to obtain rigorous upper and lower bounds onk. These variational principles are applied by evaluating them for four different types of admissible fields. Each bound is generally given in terms of various kinds of correlation functions which statistically characterize the microstructure of the medium. The upper and lower bounds are computed for flow interior and exterior to distributions of spheres.

On the image-charge model for the hydration force

The image-charge model for the repulsive hydration force in multilamellar systems of zwitterionic molecules (e.g. phospholipid bilayers) proposed by Jonsson and Wennerstrom (J. Chem. Soc., Faraday Trans. 2, 1983, 79, 19) is analysed in some detail. Some over-restrictive assumptions in their model are removed and the hydration force is calculated in a greater variety of cases. In general, the force follows a power law. The leading term for large lamellar spacing is a repulsive, zwitterionic self-image interaction. The total force for reasonably small spacings depends crucially on the zwitterionic correlation within each bilayer and may be attractive as well as repulsive. The results are very dependent on the model and change dramatically when the location of the dielectric discontinuities between water and hydrocarbon relative to the polar headgroups is varied, unless the zwitterions lie flat parallel to the interface. If the lateral compressibility is (assumed) negligible and the zwitterions are perpendicular to the lamellar plane, the force law is exponential for a very particular kind of correlation function; this was the main case considered explicitly by Jonsson and Wennerstrom. The different force laws are compared with experimental values of the forces.

A scaling method for deriving kinetic equations from the BBGKY hierarchy

On the basis of the scale covariance of correlation functions under a coarsegraining in space and time, the Boltzmann equation for neutral gases, the Balescu-Lenard-Boltzmann-Landau equation for dilute plasmas, and linear equations for the variances of fluctuations are derived from the BBGKY hierarchy equations with no short-range correlations at the initial time. This is done by using Mori's scaling method in an extended form. Thus it is shown that the scale invariance of macroscopic features affords a useful principle in nonequilibrium statistical mechanics. It is also shown that there existtwo kinds of correlation functions, one describing the interlevel correlations of the kinetic level with its sublevels and the other representing the fluctuations in the kinetic level.