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This paper presents a new diplexer design of a new-coupled composite right/left-handed (CRLH) resonator to serve the LTE applications. The realization of the diplexer is designed as coupled two zer...

Scattering from a grounded chiral slab with rough interface is studied using perturbation theory. A system of equations for zeroth and higher order solution is written, which can be solved to get c...

A lattice Boltzmann representation of the zeroth moment density closure of Hammett et al. is shown to reproduce Landau exponential decay of a perturbed density profile provided five streaming veloc...

A method for obtaining approximate bond graph models for linear time invariant (LTI) Multi-Input Multi-Output (MIMO) systems with singular perturbations is presented. The basic idea of using time-scale analysis in obtaining low-order models is to decouple the slow and fast models. This is achieved by using two-stage linear transformations. Hence, a procedure to construct decoupled bond graph models based on R-fields representing each dynamic of the singularly perturbed system is proposed.When the linear transformations are applied to the system with singular perturbations, non-linear and linear equations have to be solved for separating the subsystems. In many cases, the exact solutions of these equations are complicated, but approximate solutions can be determined and approximate models can be obtained.Thus, zeroth- and first-order solutions in a bond graph approach are proposed. The key to finding the approximate solutions is to obtain the relations of the original bond graph with a predefined i...

New discontinuity factors (DFs), i.e., individual and common DFs, for the simplified P3 (SP3) theory are proposed. In the individual DFs, two DFs are used for zeroth- and second-order angular momen...

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition., Graphical Abstract

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke’s-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover–Holian, Ju–Bulgac, and Martyna–Klein–Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs’ universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zerot...

We investigate some unusual behaviour observed while performing molecular dynamics simulations of small molecular clusters using a constrained Langevin thermostat. Atoms appear to be thermalised to different temperatures that depend on their mass and on the total number of particles in the system. The deviation from the zeroth law of thermodynamics can be considerable for small systems of heavy and light particles. We trace this behaviour to the absence of thermal noise acting on the centre of mass of the system. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. By removing the constraint, the Langevin thermostat may be restored to its intended behaviour. We also investigate a Langevin thermostat constrained to have zero total force acting on its centre of mass, and find similar deficiencies.

In this paper, we establish a continued product approximation for the gamma function: where the powers γi can be determined by a recurrence. It can be seen that one of Mortici's [A class of integral approximations for the factorial function. Comput. Math. Appl. 2010;59(6):2053–2058] results is a special case of our approximation and can be viewed as the zeroth truncation. Some numerical computations are also made to show the performance of this formula.

In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions., 13 pages, submitted for publishing

Various HN rapidly convergent schemes are proposed to speed up the slow convergence of the iterative solution of 2‐D linearized Bhatnagar‐Gross‐Krook (BGK) kinetic equation containing up to the first moments of the distribution function. The formulation of the 2‐D HN acceleration schemes is provided in a generalized manner, followed by a formal 2‐D Fourier‐mode stability analysis to determine the most efficient HN approach. The H0 method is the most efficient when the kinetic equation contains only the zeroth moment of the distribution function, while when it contains the zeroth and the first moments the most efficient approach is the H1. Although the analysis and the conclusions are restricted to the continuous form of the equations, they are indicative for the associated discrete equations.

A new S n discretization of the angular Fokker-Planck operator used in three-dimensional calculations is derived for product quadrature sets. It is straightforward to define discretizations that preserve the null space and zeroth angular moment of the analytic operator and are self-adjoint, monotone, and nonpositive-definite. Our new discretization differs from more straightforward discretizations in that it also preserves the three first angular moments of the analytic operator when applied in conjunction with product quadrature sets constructed with Chebychev azimuthal quadrature. Otherwise, it preserves only two of the three first angular moments. Computational results are presented that demonstrate the superiority of this new discretization relative to a straightforward discretization. Two-dimensional versions of the new discretization are also given for x-y and r-z geometries.

Results of using descriptors calculated with the correlation weights (CWs) of local graph invariants for modeling of anti-HIV-1 potencies of two groups of reverse transcriptase (RT) inhibitors are reported. Presence of different chemical elements in molecular structure of the inhibitors and the presence of Morgan extended connectivity values of zeroth-, first- and second order have been examined as local graph invariants in the labeled hydrogen-filled graphs. By Monte Carlo method optimization procedure, values of the CWs which produce as large values as possible of correlation coefficient between the numerical data on the anti-HIV-1 potencies and values of the descriptors on the training set have been computed. The model of the anti-HIV-1 activity obtained with compounds of training set by means of optimization of correlation weights of presence of chemical elements together with the presence of Morgan extended connectivity of first order is reasonable well model for the prediction of endpoints under con...

Hybrid differential evolution is applied to estimate the kinetic parameters of batch polymerization described by differential-algebraic equations. The dynamic behavior of the system consisted of the concentrations of the first and second initiators, the monomer conversion, the zeroth, first and second moments of dead polymer distributions and the total concentration of live polymer. The moments of dead polymer distributions and the total concentration of live polymer were in general difficult to measure in a real process. In this study, we considered that the estimation criterion consisted of some measurable data such as the concentrations of the first and second initiators, the monomer conversion, and the degree of polymerization and polydispersity. We used the worst observed error for all experiments as an objective function so that the parameter estimation problem becomes a min-max estimation problem. Several techniques were also employed to handle the estimation of kinetic parameters for comparison. Hybrid differential evolution could use five individuals to obtain a more satisfactory solution.

The moments of the impulse response are a new tool for the interpretation of transient electromagnetic data. The nth moment is the integral of the impulse response weighted by time to the nth power. The zeroth- and first-order moment are equivalent to the inductive and resistive limits and the higher-order moments place emphasis on the late time data. A good approximation to the moments can be calculated relatively easily from the measured data. Also, for some simple models, the formulae for the moments are relatively simple expressions. Hence, it is comparatively easy to invert these expressions to derive source parameters from the measured moments. For example, the conductance of a thin sheet or the conductivity of a halfspace can be derived from the low-order moments. There are no analytic expressions for the high-order moments of a half-space, so the concept of realizable moments has been introduced to allow the higher-order realizable moments to be converted to a conductivity or conductance estimate. The moment data have been shown numerically to be additive. This has two ramifications. 1) The earth can be approximated by a multiplicity of small spheres and the properties of these spheres can be inverted for. A prototype-imaging scheme which does this gives promising results. 2) The regional or background response can be subtracted from the data and the residual anomaly can be modelled. Because the modeling algorithms are fast, they can be incorporated into inversion schemes linked to database packages such as Geosoft montaj.

In this note we discuss the relationship between the underlying kinetic model and the statistical (or analytic) model used to study degradation. For small degradation rates, the zeroth, first, and second order statistical models give approximately the same fits and predictions on either the original assay scale or the percent of label claim scale. However, It is shown that the zeroth and second order statistical models artificially induce differential degradation rates across strengths when the percent of label claim response data are analyzed and poolability is not allowed across strengths. The first order model is free of this problem when the true degradation kinetics are first order. We make some recommendations in pooling stability data across strengths.

The Method of Second Moments is a unique numerical scheme developed in the early 1970s for species transport simulations. The ability of the quasi-Lagrangian method to exactly advect a quantity without numerical dispersion is one of its attractive features. The zeroth, first, and second moments correspond to the value of the quantity, the centroid, and the distribution spread within an elemental volume. Application of this method is particularly attractive for general heat transfer calculations, and provides subgrid scale accuracy even when using coarse grids. The method is simple to employ, fast, accurate, and serves as an alternative to more robust and complex methods utilizing mesh refinement techniques.

The factor Γ4(Δω) describing the intensity distribution at large detunings Δω from a vibrational band centre is calculated for classical linear rotators in a buffer monoatomic gas. A formalism developed uses the theory of moments and is appropriate for a spectroscopy of any rank. The invariant form of the interaction potential and the irreducible tensor approach are exploited to derive the third- and fourth-order Poisson brackets of spectroscopic quantities. The anisotropy of the pair distribution function is analytically incorporated in the formulas for zeroth and second moments of the torque spectra appearing in the wing distributions. By a similar technique, the relaxation rates of rotational energy and momentum are studied. Useful analytical relations are found in the fast-collision limit. Calculations performed for CO+ He and CO2+ He systems permit one to check the accuracy of the current models based on the infinite order sudden approximation and are in reasonable agreement with available experiment...

The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelen...

Solute concentrations in streams due to instantaneous slug releases are frequently influenced both by decay and by exchange with dead zones, among others. Based on the transient storage equations with first-order decay terms, explicit relationships are given for the computation of the zeroth to third temporal moments. The equations presented were applied within the framework of moment-based similarity functions which yield approximate temporal distributions of concentration. Results thus obtained were subsequently compared to finite difference solutions of the transient storage equations, in order to investigate the relationship between these approaches. Within the previously established ranges of applicability of the two similarity functions employed the comparisons indicated fairly good agreement.

Experimental and computer simulation values of the zeroth and second moments of the depolarized Rayleigh and Raman spectra of N2 are reported. A wide range of density at a fixed temperature of 50°C was covered. The density dependence of the spectral moments is due primarily to interaction-induced effects which are successfully modelled here assuming a first-order dipole-induced-dipole mechanism. The agreement between experiment and simulation is good, with the exception of spectra at state points where it appears that the ‘distinct’ term (i.e., the contribution from orientationally correlated pairs of molecules) is significant.

An analysis of the Weighted Linear Moments-Weighted Linear Discontinuous scheme (WLM-WLD scheme) for the transport equation is presented for the plane geometry case. The WLM-WLD scheme is an analogy of the WDD scheme in the class of schemes that use the zeroth and first spatial flux moments. It combines the high accuracy of nodal schemes with the main advantages of the WDD scheme such as arithmetic simplicity of algorithm and applicability to general multidimensional curvilinear geometry. The WLM-WLD scheme with the adaptive fix-up algorithm that is needed to ensure the positivity of solution gives an essential computational gain both in accuracy and speed for deep penetration transport problems compared with the WDD scheme.

Adaptive characteristic spatial quadrature schemes for use in discrete ordinates neutral particle transport computer codes in slab geometry have been introduced recently; the extension to two-dimensional Cartesian coordinates with rectangular cells is presented here. These quadratures differ from previous schemes in using strictly non-negative finite-element-like representations of the entering fluxes and scattering source, which adapt to match both the zeroth and first spatial moments. (These input moments are obtained from the boundary conditions or as output moments of the upstream adjacent cells and from the angular quadrature of the spatial flux moments in the outer iteration, respectively.) The flux throughout the cell is found by integration of the transport equation along streaming (characteristic) lines. The moments of the flux through the cell and along the exiting boundaries are then obtained. The resulting quadratures are nonlinear and strictly non-negative, while satisfying zeroth-sp...

The basic equations are derived for incompressible flow in multi-stepped annual seals. A 2-D CFD solution is used to verify the model. Exit and entrance loss factors substituted into the bulk flow solution for pressures in the cavity match the 2-D CFD solution. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation and is modeled using Moody's friction factor relationship. Linearized zeroth- and first-order perturbation equations are developed for small motion about an arbitrary position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are integrated, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynami...

A method called “Spectral K-ratio spectrophotometry” was proposed. The method takes the K-coefficient dual-wavelength spectrophotometric method as the mathematical model in order to resolve the different nth-derivative spectral data at one wavelength to determine certain two components systems that their zeroth- (absorption) and nth-derivative spectra were all interfered seriously. Examples of the application of the proposed method were given.

New data on the three-body correlation spectra obtained from collision-induced light scattering by SF6 and CF4 at 295 K are reported. The experimental zeroth and second moments are compared with calculations based on a pairwise-additive triplet cluster polarizability. Dipole-induced-dipole and electron-overlap contributions to the pair polarizabilities are considered. Comments are made on the adequacy of existing potentials for describing the scattering.

Two new slab geometry spatial quadrature schemes for use in discrete ordinates neutral particle transport computer codes are presented. The step adaptive and linear adaptive quadratures are derived as characteristic quadratures. They differ from previous schemes in using strictly non-negative finite elements representations of the scattering source within a spatial cell. These representations adapt to match the zeroth and first spatial moments of the source in the cell (which are known from the outer iteration). The resulting quadratures are nonlinear and strictly non-negative, while satisfying zeroth-spatial-moment and first-spatial-moment balances globally. They strongly ameliorate the numerical diffusion usually encountered with optically thick cells. Both schemes perform much better than conventional spatial quadratures (diamond difference, linear discontinuous, linear characteristic, linear nodal, etc.) for a deep penetration test problem, presented here. With optically thin cells, the linea...

Simulations of rare-gas gaseous mixtures taking ternary interactions into account are performed. Simulations include Ne-Ar-Kr at 300 K and He-Ar, with Ar in excess, at 165 K. The He-Ar mixtures, which were studied in more detail, give rise to a collision-induced absorption spectrum with a well-formed dip at zero frequency. The dip becomes discernible at a Ar density of 132 amagat when the ternary contribution to the zeroth moment amounts to only 2%. Interactions are assumed to be pairwise-additive.

The accuracy of the self-similarity assumption employed in the study of the grinding equation is examined in detail. This is made possible by obtaining an exact solution for any homogeneous breakup function, thereby enabling the asymptotic limit as time proceeds to be examined carefully. For the Randolph-Ranjan model of breakup, we have obtained some explicit results and these have been employed to highlight the limitations of current self-similar solutions. In particular, we note that use of a self-similar solution which depends only on the zeroth and first moment of the distribution cannot give any detailed information on the higher moments. Nevertheless, at times very soon after the start of grinding, self-similarity does lead to useful and practical asymptotic results for size distributions, since it appears that higher moments are then of less importance. Thus the reason for the success of similarity is explained and the rate of approach to this condition is given. We have also introduced a new model...

The simultaneous presence of fast and slow processes in ecological models leads to the formulation of model equations in a form amenable for the analysis by singular perturbation method. The method as originally proposed by Vasileva (1963) is applied to a specific species-resource logistic model and an algorithm useful for implementation on a digital computer is given. The solutions are obtained for zeroth, first and second order approximations. The accuracy of the solutions is examined by considering the integral-squared-error between the exact solutions and the perturbed solutions. The variation of this error with respect to the small parameter associated with the perturbation method is studied. An important result due to Tikhnov (1950) in the singular perturbation theory is illustrated. It is seen that Vasileva's singular perturbation method is a powerful analytical tool for investigations of various phenomena in the natural sciences.

The zeroth- and first-order approximations for the eigenvalue Damkohler number are determined for the steady, one-dimensional isobaric adiabatic combustion of a fuel-lean gaseous premixture under a direct one-step Arrhenius-type exothermic chemical reaction in the physically interesting limit of (1) activation temperature large relative to the hot-boundary temperature; (2) (constant) Lewis-Semenov number of order unity; and (3) fuel and oxidant stoichiometric coefficients of order unity. It is shown that, to zeroth-order of approximation, the bimolecular system behaves as a monopropellant decomposition. The dependence on the parameters of the departure of this system from such behavior, to first-order of approximation, is established.

The absolute Raman intensities and depolarization ratios of all the fundamental bands of CH2Cl2, CD2Cl2 and CHDCl2 have been measured in the gas phase. These experimental data have been included in a refinement of the vibrational potential function of the dichloromethanes. A detailed description is made of the use of the bond polarizability approach. Explicit expressions for the derivatives of the molecular polarizability with respect to the symmetry coordinates are given in terms of the zeroth- and first-order electrooptical parameters of the theory. Good agreement is found between experimental and calculated intensities. The refined electro-optical parameters compare quite well with those obtained from methane, chloroform and carbon tetrachloride. The derivatives of the molecular polarizability with respect to the normal coordinates are also given. © 1979 Taylor & Francis Group, LLC.

Within the framework of a weakly nonlinear theory, we consider, in the β-plane approximation, the nonlinear stability of a zonal shear flow. It is shown that in the regime with a viscous critical layer, the Landau constant (the coefficient of the nonlinear term of the evolution equation) is determined mainly by the interaction between the fundamental harmonic and the wave-induced mean flow distortion (the zeroth harmonic) and increases with increasing Reynolds number, R, as R ⇆. At the short-wave boundary of the instability region, the nonlinearity plays a stabilizing role irrespective of the value of the parameter β, and this includes the region in which the neutral curve has a maximum (β=4.3−3/2 for the flow u=tanh y). At the long-wave boundary, there exists a range of wave numbers for which the nonlinearity has a destabilizing effect.

We present a simple theory of the gas-phase far-infrared collision-induced absorption spectra of two molecules with tetrahedral symmetry, methane (CH4) and tetrafluoromethane (CF4). We assume that in these molecules CIA arises through octopolar and hexadecapolar induction. By neglecting the small anisotropies in the intermolecular CH4-CH4 and CF4-CF4 potentials, we can express the spectral profiles as convolutions of single-molecule free rotation spectra with intermolecular translational components. Information theory is used to estimate the ‘least biased’ form for the latter, based on our knowledge of their spectral moments (the calculation of the zeroth through sixth moments is described in an appendix). In this way we avoid the need to make questionable assumptions about the system dynamics. The computed lineshapes are in excellent agreement with the available experimental data.

It is shown that the expressions derived in a previous paper for the free energy of mixing and other thermodynamic quantities for compound forming molten alloys simplify considerably if the various interaction parameters are assumed to be small. The procedure is similar to that which for a regular solution reduces the well-known quasi-chemical expressions to the “zeroth approximation” or conformal solution expressions. Numerical application is made to AgAl.

A theory of intensity scattering from a multi-layered random medium with irregular boundaries is developed using the radiative transfer formulation. Explicit forms for the zeroth and first-order solutions are given. Special cases are shown and compared with previous results. The similarities and differences between the results of this and previous studies are pointed out. In particular, terms omitted in previous studies are indicated and previous scalar or partially scalar formulations are generalized to permit a complete polarization treatment.

The expressions for the zeroth and second moments of the three-body component of the collision-induced light-scattering spectrum are derived within the pair-potential and pair-polarizability approximations. Computer calculation of the three-dimensional integrals which appear in the moment expressions is performed for Lennard-Jones and Barker potentials of argon, krypton and xenon within the dipole-induced-dipole approximation for the pair-polarizability. The comparison of the results which are obtained with the two different potentials shows the very important role which is played by the choice of the potential in the determination of the values of the moments. An example of the applicability of the moment analysis of the three-body spectrum is also given for argon and the results compared with those of two-body.

We present a simple theory of the far-infrared collision-induced absorption spectrum of liquid methane. We assume that CIA arises through octopolar and hexadecapolar induction. By neglecting the small anisotropy in the intermolecular potential, we can represent the spectral profile as convolutions of single-molecule free rotation spectra with intermolecular translational components. Information theory is used to estimate the ‘ least biased ’ form for the latter, based on our knowledge of their zeroth and second spectral moments (the calculation of these moments is described in an appendix). In this way we avoid the need to make questionable assumptions about the system dynamics. Our theory contains no adjustable parameters, yet the computed lineshapes are in excellent agreement with the available experimental data.

For a countercurrent cooling tower subjected to a thermal disturbance by inlet air or water, theoretical equations were solved in terms of zeroth moments of air and water temperatures in the tower. Experiments were carried out by changing the temperature of inlet water at the tower top. The zeroth moments of water and air temperatures at either end of the tower predicted the relationships between the air-film and water-film heat transfer coefficients, which were then compared with the heat transfer coefficients measured from steady-state operation.

Pairwise correlations in fluids adsorbed at structureless substrates (walls) are investigated by means of a simple density functional theory. In the approach to complete wetting or drying from off bulk coexistence capillary-wave-like fluctuations lead to singularities in the total correlation function h when one or both of the particles are located in the edge of the growing film far from the wall. However these singular contributions are damped out when both particles lie close to the wall. For a hard-wall the theory yields explicit results for the zeroth and second transverse moments of h which are consistent with the predictions of exact statistical mechanical sum rules. In particular h 2(0, 0), the second moment evaluated with both particles at the wall, is proportional to the wall-fluid surface tension σ. The implications of this result for the case of complete drying at a wall-liquid-interface, where σ acquires a gas-liquid contribution from the detaching edge of the gas film, are discussed in some ...

A generalized integral transform technique is used to obtain various order analytical solutions to the problems of linear diffusion of radioactive atoms in an eroding slab, cylinder, or sphere subjected to a general boundary condition of the third kind. The zeroth- and first-order solutions obtained in this manner are compared with the exact solution; the results are highly accurate for most practical cases. The proposed technique is sufficiently versatile to cover a variety of heat and mass transfer problems in media with moving boundaries.

An analysis is performed that shows that the standard three-point difference scheme for the Fokker-Planck angular diffusion operator rigorusly preserves the zeroth angular moment, but not the first moment. As a result, the scheme does not give the exact diffusion solution in the diffusion limit. This deficiency is eliminated by means of a simple modification of the scheme. The three-point structure and positivity of the original scheme are retained in the modified scheme.

The complex formation model of Bhatia and Hargrove (BH) to explain the thermodynamic properties of compound forming A-B alloys is reformulated using a quasi-lattice picture. The formulation is explicitly carried out to an approximation where the pseudo-ternary alloy (of A and B atoms and AμBν complexes (μ, ν small integers)), envisaged in BH, is treated in the quasi-chemical approximation. It is advantageous over BH in two major respects: Firstly, it gives useful insight into the two approximations used in BH, since these follow from it by simply going to a lower (zeroth) approximation and setting the coordination number z of the alloy to be z = 2 and z = ∞. Secondly, unlike the BH approach, it provides also an expression for the short range order parameter α1 for nearest neighbours. The effect of varying z in the formulae is examined and a brief discussion of α1 is given.

In this paper we study some properties of solution of F(x,u,D2u)=f. The appearance of a null set is derived from an assumption of degeneracy at the origin, involving the dependence of F on the zeroth and second derivative terms. The non appearance of a null set is obtained by the strong maximum principle of Hopf when a strong non degeneracy assumption holds. Interior properties of solutions of F(x,u,D2u)=f on RN are also obtained under another assumption of degeneracy at infinity.

The three body correlation spectra in the collision induced light scattering by gaseous Ar, CH4, CF4 and SF6 at 295 K are reported. The zeroth and second frequency moments are compared with calculations based on a pairwise additive triplet cluster polarizability. It is found that the experimental results may be accounted for with the use of the first order dipole-induced dipole model for the polarizability. The spectra may be used to distinguish between the suitability of various intermolecular potentials; modern potentials give excellent results for Ar and CH4 and a Lennard-Jones 28-7 potential best describes the CF4 and SF6 spectra.

Several simplified models are discussed, more or less directly based upon Kirkwood's superposition approximation, currently employed in interpreting interaction induced light scattering spectra in high density simple fluids. Calculations are performed of the first two spectral moments for room temperature argon at moderate and high densities in Kirkwood's approximation using pair correlation functions from molecular dynamics and the dipole-induced-dipole pair polarizability model. Comparison with full molecular dynamics calculations indicates that at room temperature accurate zeroth and second spectral moments can be obtained using the superposition approximation and shows the limits of more simplified models in describing the density evolution of the spectral moments. The approximation is shown to work also for other induced polarizability models.

In the present paper a decomposition of the Hartree-Fock interaction energy of two closed-shell systems is given. The decomposition is obtained by performing the Hartree-Fock iterations for the supersystem in a way different from the traditional one. The procedure is called the Pauli blockade method since the interacting molecules are deformed in the field of their partners under the constraint that they cannot penetrate each others occupied spaces. The zeroth iteration of the above procedure gives the Heitler-London interaction energy and in the consecutive iterations the total energy of the supersystem is minimized letting the charge distribution of molecule A adapt itself to the presence of molecule B and vice versa, until self-consistency is achieved. It is also shown that unphysical charge transfer may occur in some methods if during mutual deformations the intersystem Pauli exclusion principle is not observed. This confirms earlier suggestions that the so called weak symmetry forcing in the perturba...

An nth-order closure is proposed between the higher-order fluctuation potentials of the mean electrostatic potentials and the potentials of the mean force. At the zeroth level the closure gives the Gouy-Chapman theory, at the first level the Loeb extension of the Gouy-Chapman theory and the Debye-Huckel theory, and at the second level the Outhwaite extension of the Debye-Huckel theory together with the equivalent problem in the diffuse double layer. Using the primitive model for the electrolyte with a plane uniformly charged electrode producing the double layer, a statistical mechanical analysis is carried out to determine the relations between the higher-order potentials of the mean force and the mean potentials. For the nth-order closure this gives a system of n + 1 differential equations in the diffuse double layer or n differential equations in the electrolyte bulk satisfied by the higher-order fluctuation potentials.

The Born model of the ionic crystal is used to calculate the energies of formation of point defects in CaF2 and UO2 in the zeroth, first and second orders. The results of calculation, to all orders, indicate that anion-Frenkel pairs are the intrinsic defects in CaF2 and are in agreement with previous calculations. In UO2 the zeroth-order calculation predicts anion-Frenkel pairs as the intrinsic defects, whereas the higher-order calculations indicate that Schottky defects are the intrinsic defects. It is concluded that Schottky defects are the intrinsic defects in UO2 with an energy of formation of about 7 ev.