A semi-empirical modified hypernetted chain equation for the one-component plasma

The hypernetted chain (HNC) equation for the one-component plasma is corrected by including a single-parameter expression for the bridge graphs whose functional form ensures that the correct long-wavelength limit of the HNC results is retained. The parameter is chosen to improve the short-range behaviour.     

The Ornstein-Zernike equation for a fluid in contact with a surface

(Molecular Physics, 1976, 31, 1291)     

On the solutions of the hypernetted chain equation inside the gas-liquid coexistence region

We present a detailed study of the solutions of the hypernetted chain integral equation inside the gas-liquid coexistence region for simple Lennard-Jones fluids. The study is performed by means of a hybrid Newton-Raphson algorithm extended to cope with complex solutions. In this way, we have unequivocally confirmed that the origin of the well-known HNC singular behavior inside the coexistence curve is linked to the onset of complex solutions. As density is increased starting from the vapor phase along isotherms inside the coexistence region, another singularity is encountered (very likely linked with the existence of a complex multiple solution point), and correlations start to diverge. Therefore, with the numerical approach here presented it is not feasible to join the liquid and vapor phases through an analytically continuous path of real and complex solutions. Finally, a study of the transition from the mean spherical approximation behavior (characterized by the presence of a spinodal divergence) to the peculiar hypernetted chain sort of singularity is also presented.     

The density profile for the Klein-Kramers equation near an absorbing wall

We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall.     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

On the summation of the virial expansion for the local density of a gas in contact with a solid

We investigate the density profile of a fluid in contact with a wall. Our analysis is based on the summation of the virial expansion for the local density and the resulting integral equation for the density profile involves the two particle direct correlation function of a non-uniform fluid.     

Calculation of static correlations in a fluid of linear molecules

Recently, both X-ray and neutron diffraction data have been obtained for liquid crystalline materials. While these results contain information about the instantaneous correlations of molecular positions and orientations in such fluids, no relevant calculations are available to aid the interpretation of the data. In this paper a formalism which may be used to describe static, molecular correlations in isotropic or anisotropic fluids of linear molecules is developed. To obtain the theory, the direct and total correlation functions of two molecules are expanded as series of spherical harmonics the arguments of which describe the molecular orientations. A relation between the expansion coefficients of these series is obtained by making use of the Ornstein-Zernike equation. It is shown that this equation may be solved in the Percus-Yevick or Optimized-Random-Phase approximations by a variational technique. This technique is used to find the total correlation function in the Percus-Yevick approximation of hard, linear molecules of various length-breadth ratios at several fluid densities.     

A note on the gaussian overlap type potential for nonspherical molecules in contact with a solid surface

Gaussian-overlap type potentials describing interactions between nonspherical molecules and a solid surface are proposed. The results are compared with predictions of the site-wall model.     

Thermodynamic calculations of linear chain molecules using a SAFT model

The recently proposed model of statistical associated-fluid theory (SAFT) by Tang, Y. and Lu, B. C.-Y. (2000, Fluid Phase Equilibria, 171, 27) is applied to phase diagram calculations of non-associating and associating linear chain molecules in which n-alkanes and n-alkenes (representing the non-associating type) and water, 1-alkanols, acids and amines (representing the associating type) are investigated. For polar molecules, the dipole-dipole interaction is taken into consideration. Overall, the proposed model yields similar accuracy to the original SAFT model, It is found that the volume and energy parameters of non-associating chain segments in the same family follow certain linear relations with the carbon number. Remarkably, these linear relations are found to hold equally well in associating chain molecules. These observations suggest that SAFT may be implemented in a more predictive manner. Furthermore, the inclusion of the contribution from dipole-dipole interaction improves the calculated values for strong polar molecules like water.     

Ground state of an impurity in a homogeneous system in the hypernetted chain approximation

The hypernetted chain theory of the ground state of a homogeneous N-particle medium NM with an impurity particle is presented. The N identical particles are fermions with spin-isospin degeneracy ν, or bosons (in the limit of ν → ∞). The ground-state wave-function of the system is assumed in the Jastrow form with central, state-independent correlation functions. Central, spin-isospin-dependent two-body interactions both in NM and between the impurity particle and the particles of NM are considered. Expressions for the ground-state energy of the system and for the separation energy of the impurity particle are derived. The simplified case of the chain approximation is also considered.     

A definitive test of the Percus-Yevick and hypernetted chain approximations in liquid metals

Pair correlation functions calculated via molecular dynamics (MD) are inverted using the Percus-Yevick and Hypernetted Chain approximations to obtain approximate pair potentials for Li and Al. The results turn out to be quite sensitive to the calculated compressibility. These approximate pair potentials are compared with the ones that were used in the MD calculation. Although some qualitative features of the original potentials are reproduced, the agreement is very poor making it clear that the PY and HNC approximations are of very little use for liquid metal calculations.     

Analytic solution of the pauli master equation for the exciton motion in the infinite linear chain with a single trap

An explicit analytic solution of the Pauli master equation for the incoherent exciton motion in the infinite linear chain with a single trap is presented. The total probability to find the exciton in the chain is also calculated.     

Asymptotic density profile of a classical fluid against a hard wall

The asymptotic density profile of classical simple fluids in contact with a hard wall is studied using the hypernetted chain approximation for inhomogeneous systems. It is shown that the one-particle distribution function tends very slowly to the density of the bulk, also in absence of a long-range wall-particle interaction, when the pair interaction between particles in the bulk varies as an inverse power at large distances.     

瑞利-泰勒不稳定性线性增长的密度梯度致稳

研究了密度梯度对瑞利-泰勒不稳定性的致稳作用,采用有限元算法求解钱得拉塞卡方程本征值问题,得到不同密度分布下理想不可压流体力学量的扰动线性增长率及扰动速度分布。扰动增长率结果与修正的Lindl公式的计算结果比较发现：扰动分布的峰值位于密度梯度标长的取值位置处,波长与密度标长可比拟时,扰动增长率显著偏离Lindl公式,而长波和短波极限情况下,数值解和Lindl公式符合较好。     

瑞利-泰勒不稳定性线性增长的密度梯度致稳

 研究了密度梯度对瑞利-泰勒不稳定性的致稳作用,采用有限元算法求解钱得拉塞卡方程本征值问题,得到不同密度分布下理想不可压流体力学量的扰动线性增长率及扰动速度分布。扰动增长率结果与修正的Lindl公式的计算结果比较发现：扰动分布的峰值位于密度梯度标长的取值位置处,波长与密度标长可比拟时,扰动增长率显著偏离Lindl公式,而长波和短波极限情况下,数值解和Lindl公式符合较好。     

Exact solution of damped nonlinear Schrödinger equation for a parabolic density profile

An exact single envelope soliton solution of the damped nonlinear Schrödinger equation in a medium with a parabolic density profile has been obtained. It is found that the condition of reflection of the soliton from the density hump is determined by its initial velocity and the scale lengths of the inhomogeneity.     

Luminescence kinetics of linear polymer molecules with chromophores randomly distributed along the chain

Luminescence kinetics of chromophores randomly attached to an isolated flexible polymer chain is studied. In the static case, when the polymer chain does not change its conformation during the donor excited-state lifetime, analytical equations are derived for the luminescence kinetics of both ideal and nonideal polymer chains. The conditions are formulated when the inhomogeneous broadening should be taken into account. For the dynamic case, the diffusion and hopping mechanisms of the polymer motion are studied.     

Luminescence kinetics of linear polymer molecules with chromophores regularly distributed along the chain

An analytical expression for luminescence kinetics of a polymer chain in the static regime is obtained for the case when the rotational motion of monomers, leading to the formation of excimers (traps of excitations), is frozen. The conditions are found when the inhomogeneous broadening of the chromophore spectra and the conformation motion of the polymer chain should be taken into account.