Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

On the motion of a three-body system on hypersurface of proper energy

Based on the fact that for hamiltonian system there exists equivalence between phase trajectories and geodesic trajectories on the Riemannian manifold, the classical three-body problem is formulated in the framework of six ordinary differential equations (ODEs) of the second order on the energy hypersurface of body system. It is shown that in the case when the total interaction potential of the body system depends on the relative distances between particles, the three of six geodesic equations describing rotations of formed by three bodies triangle are solved exactly. Using this fact, it is shown that the three-body problem can be described in the limits of three nonlinear ODEs of canonical form, which in phase space is equivalent to the autonomous sixth-order system. The equations of geodesic deviations on the manifold (the space of relative distances between particles) are derived in an explicit form. A system of algebraic equations for finding the homographic solutions of restricted three-body problem is obtained. The initial and asymptotic conditions for solution of the classical scattering problem are found.     

Method for Describing the Angular Distribution of Optical Radiation Scattered by a Monolayer of Ordered Spherical Particles (Normal Illumination)

We have developed a method for describing the angular distribution of intensity of radiation scattered by a monolayer of homogeneous spatially ordered monodisperse spherical particles normally illuminated by a plane circularly polarized electromagnetic wave. The method is based on the quasicrystalline approximation (QCA) of the theory of multiple scattering of waves (TMSW) using the multipole expansion of fields and the tensor Green function in vectorial spherical wavefunctions. The method is applied for analyzing the characteristics of radiation scattered by a partially ordered monolayer and a monolayer with a nonideal lattice. The results of calculations are compared with the available experimental data on the position of the first-order diffraction peak on the angular and spectral dependences of the intensity of radiation scattered by a closely packed monolayer with a nonideal triangular lattice of SiO₂ particles. Good conformity of the results has been established.     

On the convergence rate of a cusp-corrected damped multipole expansion for the second-order H-H+ induction energy

The improvement in the convergence rate of the damped multipole expansion for the second order H-H⁺ induction energy due to the inclusion into the first-order function of a term satisfying the electron-proton cusp condition is quantitatively investigated. Following a technique suggested by Schwartz, the multipole contributions to the energy are put in the form of series ordered by inverse powers of the quantum number l. It is shown that, for high values of l, the dependence of the leading terms is raised from l ^-4 to l ^-6 by the cusp correction.     

Three-body Coulomb Green function and the reactions with charged particles at low energies

It has been shown that the inclusion of all possible Coulomb rescatterings of three charged particles in intermediate state results in an infinite series of diagrams which have a pole located at the same place as the pole of the pole diagram. The contribution of the pole terms of such infinite series has explicitly been singled out and summed-up. Renormalization of the pole diagram amplitude due to all the possible Coulomb rescatterings of particles in intermediate state has been found. The result obtained means that the three-body Coulomb Green function entering the expression for the reaction amplitude may be written in the form of the renormalized free Green function plus the residue which behaves as in the case of short-range interactions.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Microscopic structure of <Superscript>126</Superscript>Ba in IBM terms

The yrast band of the nonaxially deformed ¹²⁶Ba nucleus is described by the Hamiltonian of the interaction boson model. Its parameters are calculated on the basis of a microscopic theory within a spherical mean field, and residual interactions that include pairing and multipole factorized forces. Each state of the yrast band is considered independently of others, allowing us to study variations in the superfluid properties of the nucleus and the quasiparticle structure of collective D phonons with spin. The calculations are performed in an expanded configuration space that includes the collective D phonon states, and noncollective states in which an additional phonon of positive parity whose spin assumes values of 0 to 6 is present along with the D phonons. It is shown that the collective Hamiltonian parameters cannot be reproduced without considering the effect of the noncollective states.     

基于原子间相互作用的低温硅单晶负热膨胀机制的研究

运用晶格热膨胀的微扰理论,推导了硅晶体的热膨胀系数与原子间两体作用和三体作用的三阶力常数之间的关系公式,在此基础上对热膨胀系数的实验数据进行拟合,计算了硅晶体内的原子间两体和三体的三阶力常数,发现三体作用的三阶力常数为正数,是硅晶体在低温下具有负热膨胀性质的根本原因。计算与分析的结果表明,运用Stillinger-Weber模型得到的三阶力常数为负数,据此不可能计算得到低温下的负热膨胀系数,因此应该对该模型进行修正。     

基于原子间相互作用的低温硅单晶负热膨胀机制的研究

运用晶格热膨胀的微扰理论,推导了硅晶体的热膨胀系数与原子间两体作用和三体作用的三阶力常数之间的关系公式,在此基础上对热膨胀系数的实验数据进行拟合,计算了硅晶体内的原子间两体和三体的三阶力常数,发现三体作用的三阶力常数为正数,是硅晶体在低温下具有负热膨胀性质的根本原因。计算与分析的结果表明,运用Stillinger-Weber模型得到的三阶力常数为负数,据此不可能计算得到低温下的负热膨胀系数,因此应该对该模型进行修正。     

Theoretical calculation of the structure of a polarizable-ionic fluid

Much theory of the structures of fluids depends on the assumption of pair-additive forces between the particles. Simulations and experiments have shown that many molten salts, molecular fluids and other systems have structures that depend sensitively on polarization of their electron clouds, or on other internal distortions. In such cases, the forces are not pair additive and the theoretical calculation of structure, expressed as a radial distribution function, g(r), is not possible using the ordinary methods. Part of the problem is that the internal structure is quantum mechanical. A theoretical method for the calculation of the structure of a fluid of polarizable particles is presented here, in a form that may be applied to any one of many structure theories in common use. The method is inspired by work on the simulation of polarizable fluids. It is applied to a simple model of a molten salt with polarizable ions. The theory is applicable to particles carrying any combination of induced electrical multipole moments, along with charges and permanent moments.     

Dielectric constant of polarizable,nonpolar fluids and suspensions

We study the dielectric constant of a polarizable, nonpolar fluid or suspension of spherical particles by use of a renormalized cluster expansion. The particles may have induced multipole moments of any order. We show that the Clausius-Mossotti formula results from a virtual overlap contribution. The corrections to the Clausius-Mossotti formula are expressed with the aid of a cluster expansion. The integrands of the cluster integrals are expressed in terms of two-body nodal connectors which incorporate all reflections between a pair of particles. We study the two- and three-body cluster integrals in some detail and show how these are related to the dielectric virial expansion and to the first term of the Kirkwood-Yvon expansion.     

Sensitivity of the three-body calculations to different effects

The bound state of few-body systems in light nuclei is studied as a three-body problem. The three-body problem is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. Separable approximations are introduced to reduce the three-body problem to a set of coupled integral equations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system³H. The main interest of the present work is to investigate the sensitivity of the three-body binding energy to different effects in the problem. For this reason, we study the dependence of the three-body binding energy of different forms of local and separable two-body potentials, on the effective range of the two-body potentials, and on the percent of theD state in the deuteron wave function. Also, we test the sensitivity of the three-body binding energy to the considered number of terms from the separable expansion.     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. General Consideration and Investigation of the Properties of the Inert Gas Solids

A crystal is described by a probability density which is not symmetric regarding the interchange of phase-space coordinates between two molecules. The set of approximate equations for one-particle distribution functions with many-body forces is derived from the LIOUVILLE equation. The expression for the HELMHOLTZ free energy and the equation of state are obtained. The developed method is applied to the determination of the thermodynamic properties of crystalline argon, krypton, and xenon. The nearest-neighbor distances, internal energies, isothermal and adiabatic compressibilities, linear thermal expansion coefficients, specific heats C_v and C_p are calculated using the pair potentials of BARKER -POMPE , of BARKER -BOBETIC , and of LENNARD -JONES , together with the AXILROD -TELLER three-body potential. The obtained results are compared with the experimental data and discussed.     

Dynamical structure factor of the Frenkel-Kontorova model

We investigate the coherent dynamical structure factorS(q, ) of the Frenkel-Kontorova model with a continued fraction expansion. The model consists of harmonically interacting particles moving in a periodic potential. It applies to quasi-one-dimensional systems where two different periods and competing interactions are important. We study commensurability effects in the collective dynamical behaviour of the particles and their manifestation inS(q, ). Our theory gives detailed results for the inelastic scattering at high temperatures. For the quasielastic peak it predicts, among other things strong oscillations of the half-width as a function of the wave vectorq. Such a behaviour can be observed in neutron scattering experiments on superionic conductors.     

A faster aggregation for 3D fast evanescent wave solvers using rotations

A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders larger than one, and becomes six times faster for large multipole orders. The method relies on a connection between the discretizations of the six integral representations, and on the fact that the Wigner D-matrices become diagonal for rotations around the z-axis. The proposed technique can also be extended to the vectorial case in two different ways, one of which is very similar to the scalar case. The other method relies on a Beltrami decomposition of the fields and is faster than the direct approach for any multipole order. This decomposition is also not limited to evanescent wave solvers, but can be used in any vectorial multilevel fast multipole algorithm.     

Semiclassical inertia of nuclear collective dynamics

For the low-lying collective excitations in nuclei, the transport coefficients, such as the stiffness, the inertia, and the friction, are derived within the periodic-orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas—Fermi approach. The multipole vibrations near the spherical shape are described in the mean-field approximation through the infinitely deep square-well potential and Strutinsky averaging of the transport coefficients. Owing to the consistency condition, the collective inertia for sufficiently increased particle numbers and temperatures is substantially larger than that of irrotational flow. The average energies of collective vibrations, reduced friction, and effective damping coefficients are in better agreement with experimental data than those found from the hydrodynamic model. The text was submitted by the authors in English.     

A variational approach to distribution function theory

We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.The conceptual approach is adapted from the cluster variation method of lattice theory.     

A three-body model of the <Superscript>11</Superscript>B nucleus

The binding energy and the rms charge and mass radii have been calculated in terms of the single-channel three-body ⁴He⁴He³H model of the ¹¹B nucleus with an expansion of the three-body wave function in a nonorthogonal Gaussian basis. Parameters of the wave function are presented and convergence of the three-body energy depending on the number of expansion terms is demonstrated.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Renormalized Perturbation Expansion in Kinetic Theory

Ladder summation techniques are applied to the recently developed c-number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T-matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell-Boltzmann statistics), the T-matrix introduced coincides with the usual T-matrix of conventional two-body scattering theory in free space. In low-temperature Fermi systems, the T-matrix differs from the reaction matrix of the Brueckner-Goldstone theory because the “healing” property of the two-body wave function does not obtain.