Approximate analytical expression for the direct correlation function of hard discs within the Percus-Yevick equation

Theory of Relaxation of Quadrupolar Nuclei in Deformable Molecules in Isotropic Solutions. Application to DNA

We investigate, within the Percus-Yevick (PY) approximation, the functional form of the direct correlation functions cij (r) for symmetric binary mixtures of hard spheres with negatively non-additive diameters Rij (i.e. two-component systems with R 11=R 22=≡R and R 12<R, at equimolar concentration). A partial exact solution is obtained when−R/2ˇ-α≡R 12-R<0 and, by introducing appropriate, simple, polynomial approximations to two functions X 12(r) and Y 11(r) contributing, respectively, to c 12(r) and c 11(r), the problem of solving the Ornstein-Zernike (OZ) integral equation is reduced to an algebraic one, i.e. to solving a system of a few (usually non-linear) algebraic equations in some unknown parameters. A very good agreement is found between our approximate solutions and the exact PY ones. Finally, a numerical Carnahan-Starling-type equation of state is presented and a successful comparison with Monte Carlo simulation data of Adams and McDonald is made.

We present a formal theory for the statistical mechanics of a nonuniform classical fluid and apply it to the hard-sphere fluid using the Wertheim–Thiele solution for the direct correlation function in the Percus–Yevick approximation. With a knowledge of the nonuniform hard-sphere fluid results, we develop a perturbation theory of nonuniform simple fluids motivated by the Weeks, Chandler, Andersen perturbation theory of uniform fluids. Using our perturbation theory, the properties of a Lennard-Jones liquid–vapor interface are calculated and compared with recent numerical experiments near the triple point. We find excellent agreement. Comparisons with other formulations are made, and the agreement is not so good.

Stability, structure, compressibility factor, excess free energy and density profile of hard prolate pear shape fluids

The pair-connectedness function and the average cluster size are determined for two different three-dimensional fluid systems using the Percus-Yevick (PY) approximation (1980). The permeable-sphere model of Blum and Stell (1980) provides a one-parameter bridge from the ideal gas (perfectly penetrable spheres) to the PY hard-sphere fluid. Two of such particles are considered to be 'bound' when their cores overlap. The percolation transition is located as a function of the interpenetrability of the particles, and is found to correspond to an average coordination number z=4. Baxter's adhesive-sphere model (1968) is also investigated in the PY approximation and it is found that at the percolation transition the average coordination number is 2. The boundary between percolating and non-percolating homogeneous thermodynamic states is determined.

Markovian frequency modulation in liquids. Analytical description and comparison with the stretched exponential approach

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Y. Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid Φ(SHS) is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. 120, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.

The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.

We discuss the problem of deriving Lévy diffusion, in the form of a Lévy walk, from a densityapproach, namely using a Liouville equation. We address this problem for a case that hasalready been discussed using the method of the continuous time random walk, andconsequently an approach based on trajectory dynamics rather than density timeevolution. We show that the use of the Liouville equation requires the knowledgeof the correlation functions of the fluctuation that generates the Lévy diffusion.We benefit from the results of earlier work proving that the correlation functionis not factorized as in the Poisson case. We show that the Liouville equationgenerates a long-time diffusion whose probability distribution density keeps amemory of the detailed form of the fluctuation correlation function, and not onlyof its long-time inverse power law structure. Although the main result of thispaper rests on an approximate expression for higher-order correlation functions, itbecomes exact in the long-time limit. Thus, we argue that it explains the failure toderive Lévy diffusion from the Liouville equation, thereby supporting the claimthat there exists a conflict between trajectory and density approaches in thiscase.

The analytical solution of Wertheim's associative Percus-Yevick approximation for an M-component mixture of associating hard spheres in the multidensity formalism is analysed. The general expressions for the Wertheim-Baxter factor correlation functions, partial structure factors and thermodynamic quantities are obtained.

Dynamics of the one-dimensional transverse Ising model

This paper considers the properties of the tap gain functions in a tapped delay line model of the orbital dipole channel. Specifically, auto-correlation and cross-correlation functions are computed for these tap functions in terms of assumed statistics for the motion of illuminated dipoles. It is demonstrated that when a certain inequality involving the transmitted signal bandwidth is satisfied, these correlation functions become identical to those which would arise from the corresponding tap gain functions of a suitably defined channel consisting of a continuum of motionless scintillating uncorrelated scatterers. In effect, this inequality sets an upper bound to the bandwidth of the transmitted signal, beyond which the orbital dipole channel may not be modeled as such a continuum of uncorrelated scatterers. Simplified expressions for tap gain correlation functions are derived for the case of large signal bandwidths, including the subcase in which the above mentioned inequality is satisfied. In the latter case the tap gain functions are shown to become mutually uncorrelated for all time shifts.

The static and dynamic properties of a dilute binary macroion mixture, where a small amount of large and highly charged spheres is immersed in a system of small spheres, are theoretically discussed. From light scattering experiments on such systems, the self-diffusion of the large spheres within the system of small spheres is essentially determined. Such systems have recently been studied by Phillies, using suspensions of highly charged polystyrene spheres. Modelling the elements of the memory function matrix by single exponentials, relating the k-dependent amplitudes and relaxation rates to the moments of the one-particle propagators, compact analytic expressions are derived for the normalized mean squared displacements and long-time self-diffusion coefficients. The moments are calculated from a generalized Smoluchowski equation and are given by integrals over the static correlation functions. Using the so-called two-component macrofluid model to calculate the static correlation functions, analytic expressions of the static partial total correlation functions in k-space are derived within the mean-spherical approximation for the binary mixture. Because of the strong dilution of the mixture, a rescaling procedure has to be used. This rescaling procedure is a simple generalization of that given by Hansen and Hayter for the one-component macroion fluid. Comparison of the theoretically calculated long-time self-diffusion of the large spheres with the experimental results of Phillies was quite satisfactory. Also, calculations of the two self-diffusion coefficients as functions of the diameter ratio and salt concentration have been performed, as well as of the normalized mean squared displacements.Key wordsColloidal suspensionself-diffusionBrownian motion

Nonprimitive electrolyte near a charged wall: generalized mean spherical approximation

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, delta-correlated in time, and scales with a positive exponent xi. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(xi) using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions: the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness, etc.) dramatically increase, thus diverging in the r-->0 limit.