Second-order Percus–Yevick theory for the radial distribution functions of a mixture of hard spheres in the limit of zero concentration of the large spheres

The radial distribution functions of a mixture of hard spheres are quite interesting when the ratio of diameters is large and the concentration of the large spheres is very small. In this regime, the radial distrbution functions change rapidly with concentration. The usual PercusYevick theory, which is adequate over most of the concentration range, fails at low concentrations of the large spheres. Values are reported of the radial distribution functions for zero concentration of the large spheres using the most accurate theory presently available, secondorder Percus-Yevick theory. Agreement with recent formulae for the contact values of these functions is very good except for the contact value for a pair of large spheres, where the agreement is fairly good. It is possible that the radial distribution function for a pair of large spheres may be a little larger than the already large values given by this recent formula.     

Cavity correlation and bridge functions at high density and near the critical point: a test of second-order Percus–Yevick theory

ABSTRACT

Cavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative near r = 0, becomes positive as r → 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY.     

Analytical evaluation of the plasma dispersion function for a Fermi—Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

Gluon distribution function from the Berger–Block–Tan form of the structure function F 2

Physics of Atomic Nuclei - We present a set of formulas to extract the gluon distribution function from the Berger–Block–Tan form of the deep inelastic structure function F 2 and its...     

Estimation of the initial density distribution in plasma–metal liners

We describe a method for estimating the initial density profile of the liner shell from experimental current and voltage oscillograms with correction of the radius of the pinch from its optical images. It is shown that the average radial profile of the initial density distribution of plasma–metal liners can be approximated by two Gaussian curves with different dispersions. The largest contribution to the main peak of the initial density distribution comes from bismuth cathode material (bismuth) ions, while the contribution to the second Gaussian curve is due to the substance of the insulator over the surface of which the vacuum arc is initiated.     

Functional derivative for the distribution function of a Λ-nucleon pair in nuclear matter

An exact expression for the functional derivative of the distribution function of a -nucleon pair in nuclear matter is derived. An approximate expression is also derived by means of the Kirkwood superposition approximation. The latter expression is subsequently used to obtain the Euler equation for the correlation functionf(r1) of a -nucleon pair in nuclear matter.     

Separability criteria based on Heisenberg–Weyl representation of density matrices

Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg–Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.     

Analytical representation of half-width for molecular ro-vibrational lines in the case of dipole–dipole and dipole–quadrupole interactions

The analytical formula for half-width of molecular ro-vibrational lines is obtained for the case of dipole–dipole and dipole–quadrupole interactions. This formula depends on the variable parameters, which have to be determined by fitting to experimental half-widths or to half-widths calculated by semi-classical methods. The application of the analytical formula to the H₂O–H₂O, NH₃–NH₃, DCl–HCl and CO–H₂O systems is discussed.     

Wigner distribution function of Lorentz–Gauss beams: a note

Stimulated by a recent investigation of the Wigner distribution function of a Lorentz?CGauss beam, we present closed-form expression for such a function at the initial plane, which is alternative to that deduced in the aforementioned investigation. Such an expression can be usefully exploited to fully account for the Wigner-plane dynamics of Lorentz?CGauss beams as far as the paraxial propagation is concerned.     

A covariant representation of the Ball–Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger–Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern–Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball–Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S   of this decomposition is not a one-loop accident, but persists at higher-loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4$N=4$ SYM theory, in the present approach relates to worldline supersymmetry.     

Analytical Solution of the Klein–Fock–Gordon Equation for the Rosen–Morse Potential

Russian Physics Journal - With the help of a successful scheme for overcoming difficulties arising for l ≠ 0 in the centrifugal part of the Rosen–Morse potential with bound states, a...     

Critical finite-size scaling of magnetization distribution function for Baxter–Wu model

The distribution function P_L(m) of the order parameter for the Baxter–Wu model is studied using blocks of linear dimension L of a larger triangular lattice. At a given temperature, we use the Metropolis algorithm for the generation of a sample of configurations on the triangular lattice. The similarities and differences of this distribution with the usual cases of Ising lattices are investigated. We conclude that the present model obeys, at the critical temperature, a finite-scaling law with the known critical exponents as expected. However, our numerical data strongly indicate that the analytic form of the scaling function does not conform to the corresponding function for the usual Ising model. An analytic expression that gives a good fit is presented.     

Estimating the entropy of liquids from atom–atom radial distribution functions: silica,beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S _e, of ionic melts with the pair correlation entropy, S ₂, shows that the temperature dependence of S _e is well described by T ^?2/5 scaling across both the normal and anomalous regimes, unlike in the case of S ₂. The residual multiparticle entropy, ΔS = S _e ? S ₂, shows a strong negative correlation with tetrahedral order in the anomalous regime.     

The Lie–Poisson representation of the nonlinearized eigenvalue problem of the Kac–van Moerbeke hierarchy

The Kac–van Moerbeke hierarchy is studied by a 3×3 discrete eigenvalue problem and the corresponding nonlinearized one an integrable Poisson map with a Lie–Poisson structure is also presented. Moreover, the 2×2 nonlinearized eigenvalue problem associated with the Kac–van Moerbeke hierarchy is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.     

An Extension of the Analytical Solution of the Ornstein–Zernike Equation with the Yukawa Closure

The analytical solution of the Ornstein–Zernike equation with one Yukawa closure of the factorizable-coefficient case is extended from the scalar-factorization case to the vector-factorization case. As a result, the scaling parameter is extended from a scalar quantity to a matrix quantity, and the scaling matrix      

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.     

The role of the bubble–bubble interaction on radial pulsations of bubbles

Using a model that with or without considering the interaction between bubbles through the radiated pressure waves, numerical simulations of cavitation bubbles have been performed in order to study the effect of the bubble–bubble interaction on radial pulsations of bubbles. Comparing the results obtained by with or without considering the bubble–bubble interaction, it is suggested that the suppression or enlargement property of expansion ratios of bubbles due to the bubble–bubble interaction largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles (in multi-bubble environment, the last two aspects can be expressed using the coupling strength). The frequency response curve of expansion ratio decreases and shifts to left due to the bubble–bubble interaction and the larger the coupling strength is, the more the left-shifting is.