One-parameter Approximation Research Articles

Toward Accurate Quantum Chemical Methods for Molecules of Increasing Dimension: The New Family of Pisa Composite Schemes.

The new versions of the Pisa composite scheme introduced in the present paper are based on the careful selection of different quantum chemical models for energies, geometries, and vibrational frequencies, with the aim of maximizing the accuracy of the overall description while retaining a reasonable cost for all the steps. In particular, the computation of accurate electronic energies has been further improved introducing more reliable complete basis set extrapolations and estimation of core-valence correlation, together with improved basis sets for third-row atoms. Furthermore, the reduced-cost frozen natural orbital (FNO) model has been introduced and validated for large molecules. Accurate molecular structures can be obtained avoiding complete basis set extrapolation and evaluating core-valence correlation at the MP2 level. Unfortunately, analytical gradients are not available for the FNO version of the model. Therefore, for large molecules, an accurate reduced-cost alternative is offered by evaluation of valence contributions with a double-hybrid functional in conjunction with the same MP2 contribution for core-valence correlation or by means of a one-parameter approximation. The same double-hybrid functional and basis set are employed to evaluate zero-point energies and partition functions. After the validation of the new models for small systems, a panel of molecular bricks of life has been used to analyze their performances for problems of current fundamental or technological interest. The fully black-box implementation of the computational workflow paves the way toward the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by experimentally oriented researchers.

Investigation of crystallographic textures in multi-level models for polycrystalline deformation using clustering techniques

The feasibility of applying clustering techniques to describe and investigate crystallographic textures by using numerical results simulated for crystallite (grain, subgrain) lattice orientations with the help of multi-level crystal elasto-visco-plasticity models is considered. The texture clustering problem is stated as partitioning a given sample of crystal lattice orientations into disjoint subsets of elements which are close to each other in a certain sense. To formalize this concept of closeness, a special pseudo-metric distance taking into account rotational lattice symmetry is introduced in the space of orientations. This distance being induced by the natural Riemann metrics determines the minimal rotation angle between the symmetrically equivalent orientations of the arguments. A heuristic algorithm based on alternating well-known clustering methods is formulated to solve the stated problem. The proposed approach allows identifying, for a polycrystalline aggregate, the regions in the space of orientations with the higher density of elements, as well as evaluating some of their effective characteristics for such regions. The developed procedure includes the following stages: dividing a sample of orientations into layers; clustering by reachability (in the sense of the transitive closure of the closeness criterion being adopted for orientations); the so-called medoid-based clustering; splitting weakly localized clusters. The application of the presented clustering technique is demonstrated by considering simple shear and axial compression textures obtained through modeling the inelastic deformation of a representative volume element for polycrystalline copper. In the examined cases, local one-parameter approximations of a given form are found for the density of distribution of the angles between orientations and medoids (conditional centers) of the related clusters. Also, the statistical significance of these approximations is tested using equiprobable intervals.

УПРОЩЕННОЕ АНАЛИТИЧЕСКОЕ РЕШЕНИЕ ЗАДАЧИ О ВНЕДРЕНИИ СФЕРИЧЕСКОГО ИНДЕНТОРА В ПОЛУПРОСТРАНСТВО С ПОКРЫТИЕМ

The contact problem of a rigid spherical punch penetration into a linearly elastic isotropic half-space with a functionally graded or homogeneous coating is considered. The problem is reduced to solving the dual integral equation. Using a one-parameter approximation of the kernel transform of an integral equation in the form of a ratio of two quadratic functions containing only one parameter, an approximate asymptotically exact solution of the problem was obtained in a simplified analytical form. The solution allows one to take into account both the elastic properties of the coating and the contribution of the substrate. In this case, the scheme for constructing an approximate analytical solution is significantly simplified in comparison to the general case. Simplified analytical expressions describing contact pressure, force, depth, and indentation rigidity are obtained. The accuracy of the solution obtained is investigated depending on the ratio of the elastic moduli of the coating and the substrate, the nature of the change in the elastic modulus, and the relative thickness of the coating. It is shown that the proposed formulas allow to achieve a sufficiently high accuracy for describing of the solution of the problem for thin and thick coatings, as well as for coatings of arbitrary thickness in the case of a relatively small difference in the elastic moduli of the coating and substrate. Using a simple one-parameter approximation makes it possible to obtain a solution to the problem in an explicit analytical form, convenient in practice for engineering calculations.

Emergence of hard X-rays at weak nonstationary processes in active regions

Using Suzaku and Reuven Ramaty High Energy Solar Spectroscopic Image (RHESSI) spacecraft data, we study the characteristics of X-ray emission of weak flares at energies when this emission is generated by fluxes of accelerated electrons. Of the 105 events recorded by a broadband monitor of the entire sky (WAM/Suzaku, with an effective area of ~800 cm2 in the energy range from 50 to 300 keV), we consider 64 B1to C3-class flares. The spectra of these events up to 30 keV are built from RHESSI data. We consider some examples of simultaneous recordings of weak flares occurring from 2005 to 2007. The radiation fluxes measured by WAM/Suzaku at 100 keV have been found to be consistent with those expected from the one-parameter approximation of spectra of the nonthermal radiation recorded by RHESSI at lower energies. The average spectral slope for all events under consideration is 4.30 ± 0.15; i.e., these rare events are significantly stricter than the majority of subflares. This can serve as proof of the fact that the particle acceleration in weak flares is more effective than was previously assumed. As in powerful events, these processes occur in the close vicinity of spots or in places where the neutral line separates hills with a large magnetic field strength.

INVESTIGATION OF THE ERRORS IN SLOAN DIGITAL SKY SURVEY PROPER-MOTION MEASUREMENTS USING SAMPLES OF QUASARS

We investigate in detail the probability distribution function (pdf) of the proper-motion measurement errors in the SDSS+USNO-B proper-motion catalog of \citet{mun04} using clean quasar samples. The pdf of the errors is well-represented by a Gaussian core with extended wings, plus a very small fraction ($<0.1%$) of "outliers". We find while formally the pdf could be well-fit by a five-parameter fitting function, for many purposes it is also adequately to represent the pdf with a one-parameter approximation to this function. We apply this pdf to the calculation of the confidence intervals on the true proper motion for a SDSS+USNO-B proper motion measurement, and discuss several scientific applications of the SDSS proper motion catalogue. Our results have various applications in studies of the galactic structure and stellar kinematics. Specifically, they are crucial for searching hyper-velocity stars in the Galaxy.

Diagnostics of dense dispersive plasmas from self-reversed atomic lines

Taking into account the effects of the dispersion of radiation on the central region of self-reversed atomic lines emitted from high-pressure strongly absorbing plasmas, the temperatures in a high-intensity discharge lamp are determined from the self-reversed lines of mercury. The diagnostic method is based on the determination of the inhomogeneity parameter using the one-parameter approximation for the relative source function. It was shown that the presence of the dispersion does not affect the diagnostic method. On the contrary, it was found that the intensity at the central line minimum is several times higher than that obtained solving the conventional radiative transfer equation, whereas the respective optical depth is several times lower. The changes in the minimum intensity and the optical depth are determined by comparing the experimental results with those obtained by numerical simulation of the studied discharge.

Effect of spatial changes in broadening on self-absorbed lines and its impact on plasma diagnostics

The influence of the spatial dependence of the line profile on the shape of a line with asymmetric self-reversal emitted from inhomogeneous discharge plasmas is investigated by solving the equation of radiative transfer using relative distribution functions for the source function and the line broadening including complex overlapping lines. The theoretical results show that the features of an asymmetric lineshape are related to the broadening mechanisms and enable us to infer from the recorded line the dominant broadening mechanism. These results are experimentally confirmed using self-reversed lines emitted from high-pressure lighting plasmas. Our detailed analysis suggests that the one-parameter-approximation (OPA) model is able to reproduce satisfactorily the spectral emissivity as in the case of a spatially constant profile. An improved technique for deducing the emissivity from line-reversal is developed and applied to plasma temperature determination of metal-halide lamps. The obtained results are optimized taking into account the functional dependence of the line width and shift on the position.

Source function approximations and their impact on the shape of self-reversed atomic lines

The shape of optically thick atomic lines emitted from inhomogeneous plasmas is calculated using both a heuristic one-parameter approximation (OPA) for the source function and the Bartels approximation. The results are compared with those obtained from solving the radiation transfer equation using selected trial source functions. The accuracy of the OPA is proved to be higher than that of the Bartels, particularly within the central line region, and independent of the equilibrium conditions in the plasma. The results open up the possibility of a realistic analysis of self-reversed lines and their application to plasma diagnostics.

Renormalization technique in designing a heat exchange apparatus

A renormalization technique of thermal design of the heat exchanger is proposed to solve the problems of designing and optimizing the gas-liquid coolant heat-exchange apparatus. In this design, the leading process is the heat transfer in the gas, and renormalization of the heat exchanger efficiency is carried out with the aim of taking into account the influence of the thermal processes in the liquid and the heat conduction of the coolant boundary. For the Nusselt criterion, the one-parameter approximation (not counting the dependences on the Prandtl number) was used. The proposed technique is economical in design, admits application of different goal functions in the optimization, and permits setting limits on the domain of variability of parameters. The efficiency of the proposed technique has been demonstrated for the problem of optimization of parameters of a ribbed-pipe heat exchanger for the facility used in investigating the interaction of a high-speed gas flow with the discharge.

Numerical validation of a self-absorption model for plasma radiation

This paper investigates the reliability of deducing the emissivity at the peaks of a self-reversed emission line from a simple empirical one-parameter approximation for the source function. The theory of spectral line shape formation owing to self-absorption in inhomogeneous axially symmetric plasma layers was reformulated and readily calculable expressions were obtained. In the case of self-reversed lines, the emissivity at the line maximum was calculated using different relative distributions for the densities of the absorbing and independently emitting atoms. The results were compared with those calculated using a source function described by a simple exponential law, the exponent of which is known as the inhomogeneity parameter. The obtained difference in the emissivity is less than 3%, which implies a difference in the (density-ratio) temperature between the line-levels better than 0.5%. Therefore, if the inhomogeneity parameter is known, the line emissivity can be deduced from the one-parameter approximation for the source function with reasonable accuracy. The effect of the structure of the plasma layer on the emissivity as well as the lateral dependence of the inhomogeneity parameter was also studied through numerical simulation.

Comments on the Scaling Behavior of Flexible Polyelectrolytes within the Debye−Hückel Approximation

Over the years, there has been much debate regarding the conformational behavior of flexible polyelectrolytes with electrostatic interactions described by the D bye-Huckel approximation. In particular, the electrostatic persistence length has been reported to depend both quadratically and linearly on the screening length as well as having no consistent power-law dependence at all. On the basis of simulation results together with a careful analysis of analytical approaches, including Odijk-Skolnick-Fixman (OSF) theory, variational calculations, and renormalization group results, it is possible to present a consistent picture, which contains a better understanding of the true behavior as well as an explanation for the diverse results. The projection length of long chains can be described by power laws in three regimes, and an expression by Odijk is qualitatively correct in two of these regimes. Scaling arguments based on OSF theory and excluded volume considerations give good agreement with the third power law, but the underlying assumptions are not entirely correct. More than one parameter is required to describe the internal chain behavior, which is characterized b short-range flexibility and long-range stiffness. Still, most analytical approaches end up in one of two one-parameter approximations, either an OSF-like perturbation expansion around a rigid-rod state or a Flory-type variational calculation based on an unperturbed chain. The latter describes at best the short-range behavior. A field-theoretic renormalization group treatment, which has suggested that there should be no power law behavior, is not valid in three dimensions. Previous support from simulation results were obtained through an unfortunate mistake. (Less)

High pressure DSC investigations on n-alkanes, n-alkane mixtures and polyethylene

A high pressure cell for a power-compensated DSC is presented, allowing measurements at pressures up to 500 MPa. With the aid of this apparatus, n-alkanes, binary n-alkane mixtures, and two linear polyethylenes have been investigated. The fusion temperature and the heat of fusion have been measured for different n-alkanes in the pressure region between normal pressure and up to 500 MPa. For five eutectic and non-eutectic binary mixtures, the liquidus and solidus temperatures were determined. It is possible to describe the mixing behaviour of n-alkanes with the one-parameter approximation derived by Porter. The increase of the Porter parameter with pressure implies decreasing miscibility at higher pressures. From the Porter parameter the critical point can be calculated. Thus, it can be seen that n-alkanes which build mixed crystals at normal pressure demix at higher pressures. From these results, it can be concluded that the same is true for polyethylene.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ‘‘linear’’ approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier’s principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

A One-Parameter Integral Method for Turbulent Transpired Boundary Layer Flow

This paper presents the development of a practical one-parameter integral method for transpired turbulent boundary layer flow. The method involves the use of one-parameter polynomial approximations for total stress and the solution of the familiar integral momentum equation. The method is compared with experimental data and numerical solutions for a range of near equilibrium boundary layers.

Generalized reduced-potential curve method and its applications.

The generalized reduced-potential curve (GRPC) is defined and analyzed. A special form of the GRPC formula is defined with respect to the reduced-potential curve (RPC) employed previously (parametrized formula). It is shown that the definition of the reduced potential used by Ferrante et al. [Phys. Rev. Lett. 50, 1385 (1983)] and Tellinghuisen et al. [Phys. Rev. A 39, 925 (1989)] is equivalent to the old definition of Frost and Musulin (FM) [J. Am. Chem. Soc. 76, 2045 (1954)] that is obtained from the GRPC as a limit case. It is further shown that the FM reduced potential cannot be used for a systematic comparative study of the potentials of diatomic molecules (which, however, may be successfully made in the RPC scheme), nor can the FM formula be employed to obtain accurate approximations of the potentials. On the other hand, it is demonstrated by a series of examples that very accurate approximation methods for the extensions of the potentials may be defined with the use of the GRPC formula in the framework of the RPC scheme. A parametrized RPC formula appears to be a good GRPC formula: For the inner wing, the one-parameter approximation already leads to a degree of accuracy that seems satisfactory also to a spectroscopist (limit of error in the internuclear distance less than 0.001 \AA{}). One-parameter approximations of potentials published previously are evaluated and shown to have reached a satisfactory degree of accuracy also in the outer wing (limit of error in energy less than 3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). The GRPC method is also employed to obtain an essentially more accurate approximation from theoretical ab initio calculated potentials. The potentials obtained with the aid of the GRPC method may then be used for the calculation of the spectra.

Nonlocal transport models of the self-consistent potential distribution in a plasma sheath with charge transfer collisions

Plasma sheaths are often assumed to be collision free; however, high-voltage cathode sheaths are typically thicker than the mean free path for charge transfer collisions at pressures encountered in glow discharge processing equipment (greater than 10 mTorr). In this paper, the potential distribution in a plasma sheath is determined by solving Poisson’s equation self-consistently using a kinetic theory nonlocal ion transport model for charge transfer collisions. The relationship between the potential distribution, ion flux, and thickness of a plasma sheath is presented for arbitrary values of the sheath thickness relative to the mean free path for charge transfer. The results may be used to estimate the ion flux from measurements of the sheath thickness and potential drop across the sheath. Ion energy distribution functions and a one-parameter approximation to the numerically determined potential distribution are also presented. These results apply to rf discharges in a time-averaged sense when the ion sheath transit time is much longer than the rf cycle time, and they apply to high-voltage cathode sheaths in ‘‘abnormal’’ dc and low-frequency rf discharges. The present model is compared to earlier self-consistent sheath models, including the collision-free approximation, the local mobility model, and a nonlocal fluid approximation known as the viscous drag model.

Practical means of cancelling the differential phase contribution to rain crosspolarisation at 10 GHz and above

At certain frequencies, removal of the differential phase contribution to rain-induced microwave crosspolarisation may produce adequate crosstalk improvement in dual-polarised links. Rotating section polarisers are shown to be capable of this removal in the presence of differential attenuation, and one-parameter approximations to the operation are shown to exist.

The characterization of order in nematic liquid crystals

It is pointed out that the usual one-parameter approximation for the order parameter tensor in nematic liquid crystals is not always adequate, and that a two-parameter description is indicated by experiments. From previously published data we find that for p-azoxyanisole at 120°C, the two parameters have the values; S ¯ = 0.52, D ¯ = 0.07, where S ¯ is the usual nematic order parameter and D ¯ describes the difference in the tendencies of the two transverse molecular axes to be oriented along the average nematic director.

The pressure dependence of theE 2 reflectivity peak and of the dielectric constant in III–V semiconductors

The functional dependence on pseudopotential form factors of the Penn gap related to theE2 reflectivity peak is used to calculate the pressure dependence ofE2 and of the static electronic dielectric constant in III–V semiconductors. In a one-parameter approximation only the pressure coefficient of one Fourier coefficient of the pseudopotential is fitted to experimental values of the pressure dependence ofE2 in group-IV semiconductors and then taken over to III–V compounds. We find a decrease of the dielectric constant with pressure. The comparison of our results with those experimentally known supports strongly our method.

Further theoretical investigation of the laminar boundary layer overrotating blades and yawed infinite wings.

In this paper the problems of the laminar boundary layer on rotating blades and yawed infinite wings have been considered theoretically by using the parametric method proposed by Loitsianskii. The spanwise boundary-layer equations in both cases have been reduced to universal form by transferring the parameters expressing the influence of external conditions characteristic of each particular problem to the number of independent variables. The universal partial-differential equations in the one-parameter approximation are solved numerically by an implicit finite-difference scheme on an IBM system 360 computer. Numerical computations for rotating blades reported in this paper are for symmetrical profiles at zero angle of attack rotating steadily with uniform angular velocity, though the analysis permits the use of more general cambered and nonzero angle-of-attack profile shapes. The solutions obtained are valid for all wing profiles satisfying the criteria of the independence principle.