Pair correlations in scale-free networks

Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi－Albert (BA) scale-free model with both analytical results and simulations, and find two neighbouring regions, a disassortative one for low degrees and a neutral one for high degrees. The average degree of the neighbours of a randomly picked node is expected to diverge in the limit of infinite network size. As a generalization of the concept of correlation, we also study the correlations of other scalar properties, including age and clustering coefficient. Finally we propose a correlation measurement in bipartite networks.     

Pair correlations in a ferromagnetic colloid

We discuss some properties of the equation of state and of the static correlations for spherical ferromagnetic grains, at thermal equilibrium, in a passive fluid. At high external fieldsH, low concentrations, and not too high temperatures, the grains tend to formchains along the directions ofH. In zero field (but otherwise identical conditions), some chains are still present but oriented at random and in competition with closed rings and clusters. Various experimental methods which could give information on these chain structures are listed.     

Structural-acoustic analysis of a nanodispersed magnetic fluid

Results of investigations into the dispersed composition of a magnetic fluid based on the measured dependence of the amplitude of the acousto-magnetic effect on the magnetic field strength are considered. The results obtained are compared with the data of atomic force microscopy and magneto-granulometric analysis.     

Non-gaussian velocity correlations in fluids

Several molecular dynamics experiments in monoatomic fluids indicate that the velocity v of a tagged particle has a clear non-Gaussian behaviour: here we present typical simulation data obtained for <v ²(0)v ²(t)>. We have previously found that at long times these non-Gaussian features can be explained in terms of a non-linear Langevin equation developed by Mori, Fujisaka and Shigematsu. Here we show that the latter approach can be the long-time version of the reduced model known as the non-linear itinerant oscillator. In principle, such a model can also reproduce the non-Gaussian behaviour at short times, as found in the simulations and confirmed by the proper sum rules. The reduced model is numerically solved in a particular one-dimensional overdamped case and the main features present in the computer experiment are found to be qualitatively reproduced.     

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) ? 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.     

Pair interactions of heavy vortices in quantum fluids

The dynamics of quantum vortex pairs carrying heavy doping matter trapped inside their cores is studied. The nonlinear classical matter field formalism is used to build a universal mathematical model of a heavy vortex applicable to different types of quantum mixtures. It is shown how the usual vortex dynamics typical for undoped pairs qualitatively changes when heavy dopants are used: heavy vortices with opposite topological charges (chiralities) attract each other, while vortices with the same charge are repelled. The force responsible for such behavior appears as a result of superposition of vortices velocity fields in the presence of doping substance and can be considered as a special realization of the Magnus effect. The force is evaluated quantitatively and its inverse proportionality to the distance is demonstrated. The mechanism described in this paper gives an example of how a light nonlinear classical field may realize repulsive and attractive interactions between embedded heavy impurities.     

Decay of angular correlations in hard-sphere fluids

The decay of the collisional contribution to the shear-stress autocorrelation function is shown to be inconsistent with at ^–3/2 inverse-power law. The decay of the self part (a combination of pair and triplet correlations) indicates a stretched-exponential decay with a density-independent exponent. The pair contribution by itself also shows stretched-exponential behavior in both two and three dimensions, with different, but still density-independent, exponents. At very long times this stretched-exponential decay of the pair correlations switches over to an algebraic decay, consistent with the diffusional separation of pairs of particles.     

Quantum decay law and correlations in fluids

Decay of classical correlations, of the type of velocity autocorrelations in fluids, is treated analytically by methods of the quantum theory of decay, and conditions are obtained for the occurence classically of initial stationarity and nonexponential long time tails.     

Pair correlations and interaction energies in FePd single crystal

Diffuse neutron scattering measurements were carried out in a FePd single crystal at 1020 K in the (100) and (110) reciprocal planes. The diffuse intensity is nearly symmetric, showing that the static displacements are small. A set of displacement and short-range order parameters have been fitted to the measured data using a least square procedure. The short-range order parameters have been used in conjunction with an inverse cluster variation method to deduce the pair interaction energies. A strong attractive interaction between second nearest-neighbour like atoms is found.Received: 11 August 2004, Published online: 12 October 2004PACS: 61.12.Ex Neutron scattering - 64.60.Cn Order-disorder transformations - 61.66.Dk Alloys     

Pair correlations in a finite-temperature 1D Bose gas

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature "fermionization" through the measurement of the rates of two-body inelastic processes, such as photoassociation.     

Pair correlations of an expanding superfluid Fermi gas

The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.     

Protein-stabilized magnetic fluids

The adsorption of bovine serum albumin (BSA) and egg yolk phosvitin on magnetic fluid particles was investigated. Incubation mixtures were prepared by mixing an alkaline suspension of tetramethylammonium-coated magnetite cores with protein solutions at various protein/Fe₃O₄ ratios, followed by dialysis against a 5 mM TES buffer (pH 7.0), after which separation of bound and non-bound protein by high-gradient magnetophoresis was executed. Both the kinetic profiles as well as the isotherms of adsorption strongly differed for both proteins. In case of the spherical BSA, initially, abundant adsorption occurred, then it decreased and—at high protein concentrations—it slowly raised again. In contrast, with the highly phosphorylated phosvitin, binding slowly started and the extent of protein adsorption remained unchanged both as a function of time and phosvitin concentration. Competition binding studies, using binary protein mixtures composed of equal weight amounts of BSA and phosvitin, showed that binding of the latter protein is ‘unrealistically’ high. Based on the geometry of the two proteins, putative pictures on their orientation on the particle's surface in the various experimental conditions were deduced.     

Parametric resonance in magnetic fluids

A new resonance effect in the nonlinear behaviour of magnetically anisotropic objects in an alternating external magnetic field is proposed. Ferromagnetic particles with a “frozen” magnetic moment (due to a strong magnetic anisotropy), when located in an external alternating magnetic field, are able to rotate (or vibrate) and to transfer energy from the external field to the medium. The numerical solution of the appropriate parametrically driven nonlinear equation shows all types of nonlinear dynamic behaviour, including transition to chaos. The sensitivity of the proposed phenemenon could be used for an experimental analysis of the size distribution of the ferromagnetic particles in a ferrofluid or of the size of “magnetic holes”.     

Buoyancy forces in magnetic fluids

The ponderomotive force on a macroscopic body in a magnetic fluid is calculated by a hydrodynamic approach. The resulting equations are generally valid, neither small susceptibilities nor stationarity are assumed. The simple and widely-used formulaV(M-M ^bg )H is recoverd in linear order of ; magnetostrictive effects are shown to contribute in the order ³. The expressions derived here are definite and unambiguous, they do not depend on whether one starts from a theory in terms ofH, or in terms ofB: the correct evaluation of the contribution dV[-p] resolves the apparent contradiction between the force density expressions ₀ MH, orMB.     

Many-body correlations in the problems of electrodynamics of fluids

This paper presents a review of the theory of the many-body correlation phenomena in fluids, in which the collective character of the fluctuations is caused by the long-range interaction of electrodynamic origin. The procedure of the statistical mechanical averaging of the microscopic electrodynamic equations is developed for a classical system of the interacting polarizable molecules with a subsequent account of the molecular correlations. As a result an effective expansion for the refractive index is obtained. The dependence of the refractive index on the thermodynamic parameters near the critical point is investigated using the scaling-law asymptotics for the many-body correlation functions. A molecular theory of the multiple light scattering is suggested. A method of evaluation of the many-body any-order scattering intensity in the critical region is described. Using a resummation procedure, similar to that developed for the light propagation problem, the correlation function expansion is obtained for a classical system of charged and neutral particles, correlations due to the short-range forces are taken into account. The expansion gives series in terms of the effective “dressed” electrostatic potential containing no long-range Coulomb divergencies, nor short-range ones.     

Shear stress correlations in hard and soft sphere fluids

The shear stress autocorrelation function has been studied by molecular dynamics simulation using the q^?n potential for very large n. The results are analysed and interpreted here by comparing them with the shear stress response function for hard spheres. It is shown that the hard sphere response function has a singular contribution, and that this is reproduced accurately by the simulations for large n. A simple model for the stress autocorrelation function at finite n is proposed, based on the required hard sphere limiting form.     

Decay of correlations in classical fluids with long-range forces

We show with simple arguments that, as a consequence of the Poisson equation, the correlations of a charged system at equilibrium decay faster than any inverse power, if they are integrable and monotonous at infinity. For all other longrange systems (with potential(x)b¦x¦^–s , ¦x¦ , 0v,s} 2), the decay is bounded below by an inverse power.Partially supported by the Swiss National Foundation for Scientific Research.     

Spin-glass-like magnetic ordering in Zn substituted magnetite magnetic fluids

Electron spin resonance (ESR) spectra of magnetic fluids involving polydispersed Zn(0.5)Fe(0. 5)Fe(2)O(4) (FZ5) and Zn(0.7)Fe(0. 3)Fe(2)O(4) (FZ7) nanomagnetic particles are scanned from 4.2 to 300K. The FZ7 fluid exhibits certain distinct features below 40K which are different from FZ5 fluid. These include (i) an isotropic shift in resonance field in zero-field-cooled ESR study, (ii) deviation of resonance field from sin(2)theta behavior (where theta is the angle between axis of the particle and field) in field cooled (FC) sample and (iii) abrupt increase in anisotropy field for FC sample. The results are analyzed in light of the core-shell model for nanomagnetic particles.     

Sound velocity measurements in magnetic fluids

Sound velocity measurements were made in a kerosene-base magnetic fluid. Both pulse-echo and c.w. resonance techniques were used for frequencies from 2 to 45 MHz. The resulting value of velocity was 6 percent lower than that obtained for the kerosene.