One-component-plasma: Going beyond Debye-Hückel

Using field-theoretic methods, we calculate the internal energy for the One-Component Plasma (OCP). We go beyond the recent calculation by Brilliantov [N. Brilliantov, Contrib. Plasma Phys. 38, 489 (1998)] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter , the effect of the higher-order terms is small and that the final result is not improved relative to the Gaussian theory when compared to simulations. Received 12 April 1999     

Accuracy and convergence of a variational theory of nuclear matter for ν6 models

A number of higher-order terms in a previously proposed variational theory of nuclear matter are examined to establish the accuracy and convergence of the method. Numerical results for four semirealistic ν₆ model interactions, which include central, spin, isospin and tensor components, are reported. Although individual higher-order terms are substantial (> 1 MeV) they are much smaller than the corresponding lower-order terms, indicating good convergence of the theory. The higher-order terms also tend to cancel out, and three of the four ν₆ models show little net change in their E(k_F) curves, compared to previous work. The method is believed to have an error ?1 MeV for k_F ≦ 1.6 fm^?1.     

On the calculation of pressure-broadened linewidths for symmetric-top molecules using the modified Anderson theory

An approximation, accurate to better than 0.5%, to the Anderson-Tsao-Curnutte theory of linewidth is presented. This approximation is shown to be suitable for calculating linewidths of symmetric top molecules where dipole-dipole forces are dominant, but higher-order multipole terms are not negligible. Some insight is gained as to the relative importance of various types of collisions between interacting molecules from this approach to the calculation of the spectral linewidths for rotational states of molecules. Experimental results for CH₃³⁵Cl and CH₃¹²⁷I are presented for comparison with the calculated results.     

The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.     

Hyperfine structure in hydrogen and helium ion

QED theory of the hyperfine splitting of the 1s and 2s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_HFS(2s)−E_HFS(1s). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α(Zα)³E_F and examined the recoil contribution in order (Zα)³m/M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 10⁸) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.     

Parametrized post-post-Newtonian (PP2N) formalism for the solar system

An extension of the parametrized post-Newtonian (PPN) formalism to third order in the expansion parameterm/r is used to derive analytical expressions accurate to the same order for the motion of test particles and photons in the presence of the gravitational field of the sun represented by a static, isotropic metric. The consequences of including higher-order terms are discussed in relation to the so-called classical gravitational tests for the case of general relativity theory. Present observational or experimental data are not accurate enough to detect variations due to the inclusion of higher-order terms but a planned solar probe experiment may provide information that would make such detection possible.     

IDeC(k): A new velocity reconstruction algorithm on arbitrarily polygonal staggered meshes

We propose a novel algorithm for velocity reconstruction from staggered data on arbitrary polygonal staggered meshes. The formulation of the new algorithm is based on a constant polynomial reconstruction approach in conjunction with an iterative defect correction method and is referred to as the IDeC(k) reconstruction. The algorithm is designed for second order accuracy of the reconstructed velocity field and also leads to a consistent estimate of velocity gradients. Accuracy, convergence and robustness of the new algorithm are studied on different mesh topologies and the need for higher-order reconstruction is demonstrated. Numerical experiments for several cases including incompressible viscous flows establish the IDeC(k) reconstruction as a generic, fast, robust and higher-order accurate algorithm on arbitrary polygonal meshes.     

Application of a time-dependent density-matrix formalism

An extended time-dependent Hartree-Fock theory which includes the effects of nucleon-nucleon collisions is presented and applied to the small-amplitude quadrupole motions of¹⁶O and⁴⁰Ca. The collision term of the theory includes not only the Born term but also higher-order terms. It is found that the higher-order terms are essential to the damping of the motions.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

A variable kinematic Ritz formulation for vibration study of quadrilateral plates with arbitrary thickness

A new variable kinematic Ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented. Carrera's unified formulation and the versatile pb-2 Ritz method are properly combined to build a powerful yet simple modeling and solution framework. The proposed technique allows to generate arbitrarily accurate Ritz solutions from a large variety of refined two-dimensional plate theories by expanding so-called Ritz fundamental nuclei of the plate mass and stiffness matrices. Theoretical development of the present methodology is described in detail. Convergence and accuracy of the method are examined through several examples on thin, moderately thick, and very thick plates of rectangular, skew, trapezoidal and general quadrilateral shapes, with an arbitrary combination of clamped, free and simply supported edges. Present results are compared with existing three-dimensional solutions from open literature. Maximum and average differences of various higher-order plate theories and three-dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters.     

Invariant Higher-Order Variational Problems

We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our approach formulates Euler-Poincaré theory in higher-order tangent spaces on Lie groups. In particular, we develop the Euler-Poincaré formalism for higher-order variational problems that are invariant under Lie group transformations. The theory is then applied to higher-order template matching and the corresponding curves on the Lie group of transformations are shown to satisfy higher-order Euler-Poincaré equations. The example of SO(3) for template matching on the sphere is presented explicitly. Various cotangent bundle momentum maps emerge naturally that help organize the formulas. We also present Hamiltonian and Hamilton-Ostrogradsky Lie-Poisson formulations of the higher-order Euler-Poincaré theory for applications on the Hamiltonian side.     

Local deformation and the structure of the Stark splitting of rare-earth ions

A model for describing the relaxation of ligand ions close to a defect when impurity ions are introduced into a crystal is proposed and verified. The approach assumes that ionic displacements into new equilibrium positions can be regarded as fundamental parameters of impurity crystals that can be determined from experimental data concerning the energy structure of the impurity ion. Direct calculations for rare-earth impurity ions using crystal-field theory showed that the energy spectrum of these ions strongly depends on the equilibrium positions of the nearest matrix ions surrounding them. The results of the calculations are compared with the available experimental data. The parameters of the theory are determined. The possibility of applying this approach to the study of other systems is discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1194–1199 (July 1999)     

Vibrational analysis of nitrosamine,a molecule with an almost constant potential along the inversion coordinate

ABSTRACT

The fundamental vibrational transitions of nitrosamine and its doubly deuterated isotopologue have been computed by vibrational configuration interaction theory including up to 6-tuple excitations. The potential energy surface has been represented by an n-mode expansion up to 4-mode couplings terms obtained from explicitly correlated coupled-cluster theory, CCSD(T)-F12a. Very good agreement with experimental data has been been achieved and a number of new assignments is provided.     

Density of states near the Anderson transition in a space of dimensionality d=4−ε

Asymptotically accurate results have been obtained for the average Green’s function and the density of states in a Gaussian random potential for dimensionality of space d=4−ε over the entire energy region, including the vicinity of the mobility threshold. For N∼1 (N is the order of the perturbation theory) only parquet terms corresponding to higher terms in 1/ε are taken into account. For large N all powers of 1/ε are taken into account with their coefficients calculated in the main asymptotic limit in N. This calculation is performed by combining the condition of renormalization theory with the Lipatov asymptotic limit. Zh. éksp. Teor. Fiz. 111, 1896–1914 (May 1997)     

Density functional theory for chiral nematic liquid crystals

ABSTRACT

In this note, the density functional theory for chiral nematic liquid crystals is expressed in terms of rotational invariant expansion coefficients of the pair-excluded area at fixed separation. This modification from the standard approach, without making any additional assumptions, yields a more efficient procedure for minimising the free energy, as well as providing insight into the origins of the effect away from the long-pitch limit.     

Tricritical Directed Percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations. PACS numbers: 05.70.Ln, 05.50.+q, 05.65.+b     

Quantum-classical correspondence in response theory

The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the h expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.