An analytical approach to wire-to-cylinder corona discharge

In the present paper, an analytical approach is proposed to determine the radial distributions of electric field, electrons, ion densities and temperature of a DC corona discharge in wire-to-cylinder geometry, using oxygen as feed gas. The current–voltage (CV) characteristic measured in experiments is used as an input in the calculation. The objective of this work is to provide approximated analytical solutions of the corona discharge with low computational cost, which can be useful in different technological applications, such as the generation of ozone or the decomposition of pollutant gases. The predictions of the analytical model are compared with the results obtained from a much more complete numerical simulation.     

An analytical approach to discharge circuits in gas lasers

Summary An analytical method for solving equations applied to circuits whose resistance varies according to an exponential decay law is proposed and applied. The solution is given in terms of generalized hypergeometric functions. To speed publication, the authors of this paper have agreed to not receive the proofs for correction.     

Autler-Townes triplet spectroscopy: An analytical approach

In Ref. [Opt. Commun. 273, 464-472 (2007)] we studied Autler-Townes triplet spectrum. The presented results were not easy to display in readable and transparent form because the operating physical mechanism is hidden by the algebraic complexity. Here we present analytical results in a very simple and interpretable form. These results enable us to get a new insight into the interference mechanism in a quiet clear manner. We have given a new dimension to the problem in calculating the emission spectrum by state vector method. New estimates are given to measure the spectroscopic parameters in analytical fashion. The interference mechanism in the excited three decaying dressed state is effectively explored which splits the single Lorentzian peak to three spectral components due to two dark lines. The width of each spectral component can be narrowed to up to 0.05Γ.     

Relativistic spherical polytropes: An analytical approach

Using the technique of Padé (2, 2) approximant we present, in this paper, an approximate analytical solution to the field equations of general relativity for time-independent, spherically symmetric systems in which the pressureP and density are related by a polytropic equation of state:P = K ^1+1/n. The boundary values of coordinate radius ₁, for polytropic indicesn = 0, 1.0 (0.5) 3.0, are given in Table I. Table II contains the values of other physical parameters, (₁) (mass), (the density concentration), and 2GM/c²R (the ratio of gravitational radius to the coordinate radius) forn = 0 and 1.Work done at Azerbaijan State University, Baku, USSR (1977–79).     

双离子成份等离子体的离子声色散关系

以离子温度与电子温度之比为参数,将等离子体介电函数作展开,由此解析地求解了双离子成分等离子体的离子声快、慢波模的色散关系。与现有的其它解析理论相比较,所得到的解析公式更加准确。     

双离子成份等离子体的离子声色散关系

 以离子温度与电子温度之比为参数,将等离子体介电函数作展开,由此解析地求解了双离子成分等离子体的离子声快、慢波模的色散关系。与现有的其它解析理论相比较,所得到的解析公式更加准确。     

An analytical approach to the design of electrodes in high-power, fast-transverse-flow lasers

Usually, the design of the electrodes of fast-transverse-flow CO₂ lasers relies more on experimental data than on theoretical analysis. Traditional systems sustain a stable, high-power discharge but the current distribution generates a peaked, non-uniform small-signal-gain pattern. We present a theoretical model suitable for the design of electrodes that achieves a quasi uniform gain distribution. The analysis, based on a two-temperature model and the gas-transport equations, computes the electron density that supports a flat gain pattern. Combining the desired electron density with the electron-balance equations, the model determines the required electric field. The results were used to design a new set of electrodes for a home-made fast transverse flow CO₂ laser. A stable, large volume discharge () with very good uniformity was obtained. The resulting gain distribution was registered in a bi-dimensional map. The peak gain rose from , attained with the old electrode set, to with the new one and the gain showed a homogeneous profile.     

An analytical approach to the distribution function of electrons in the molecular oxygen discharge

Analytical expressions for the electron distribution function and the kinetic coefficients in the molecular oxygen glow discharge are given. The relative importance of the various collisional processes in evaluation of some experimentally measured quantities is discussed as well as the validity of the present results.     

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams for the massless ϕ ³ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of the Lipatov integrable chain model. The text was submitted by the authors in English.     

An analytical superposition approach to wall heat conduction under arbitrary temperature perturbations for air-conditioning applications

An analytical solution is derived for the transient wall heat conduction problem under arbitrary outdoor air temperature perturbations. This is obtained by expanding the arbitrary perturbation in a Fourier series, consisting of a step function and an infinite sum of cosine and sine functions. The analytical solutions in the cases of step, cosine and sine temperature perturbations are derived separately from each other and are then superimposed to produce the resultant solution. Simple linear expressions are derived, which express the maximum indoor heat flow provoked by the arbitrary temperature perturbation in terms of parameters characterizing the perturbation. Such simple expressions are very useful in air-conditioning calculations for predicting peak loads and sizing heating or cooling equipment.     

Modeling interdiffusion in semiconductor distributed Bragg reflectors: An analytical approach

The effect of interdiffusion on some important optical properties of semiconductor distributed Bragg reflectors (DBRs) has been successfully modeled by simple analytical expressions. An analytical expression for the coupling coefficient κ$\kappa$ was derived as a function of diffusion length. This expression allows the reflectivity, stop bandwidth, and penetration depth to be modeled for diffused DBR structures. A 19-period GaAs/AlAs DBR centered at 950 nm was used to test and validate the model. It has been shown that the obtained results agree very will with those reported earlier using the transfer matrix method. As so, the model may provide a simple, versatile, and rapid technique for the analysis of diffused DBRs composed of any material system.     

An analytical molecular orbital approach in tetrathiafulvalene tetracyanoquinodimethane (TTF-TCNQ)

In low-dimensional molecular crystals exhibiting the Peierls instability, intercolumnar interactions play an important role in electrical conduction. In this work, we propose an efficient method based on molecular orbital theory for studying the Peierls instability in molecular crystals composed of mixed-valence complexes. A perturbational approach to general N-merized systems is incorporated and applied to tetrathiafulvalene tetracyanoquinodimethane (TTF-TCNQ) crystals. From the results of the calculations, a mixed state of several commensurate distortions is proposed as another aspect of the incommensurate distortion in TTF-TCNQ under atmospheric pressure, and TTF^+0.5–TCNQ^?0.5 crystal is found to be expected as an electronic conductor under high pressure.     

Distance-dependent connectivity: Yet another approach to the small-world phenomenon

We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of people in a very simple manner. The acquired results agree with the well-known presence of the small-world phenomenon in human relationships. They indicate that this feature can be understood merely as a consequence of the probability composition. We also examine how this phenomenon evolves with the development of human society.     

An exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions

A comprehensive analytical technique is developed for the free vibration analysis of rectangular plates with discontinuities along the boundaries. For illustrative purposes a solution is obtained for plates with edges partially clamped and partially simply supported and plates with edges partially and partially simply supported. A vast array of first mode eigenvalues is provided for these families of plates. Solutions to the equations are obtained by exploiting a mathematical technique described by the author during an earlier publication. It is shown that eigenvalue matrices are easily generated for a wide range of plates with discontinuities in boundary conditions.     

Laser heating: an analytical approach to the theory

The theory of pulsed and scanned laser beams is developed and the results are shown to agree with similar analyses by other authors. A new expression, however, for the temperature rise caused by a very small laser spot agrees well with recent experiments.     

An analytical study of droplet combustion under microgravity: Quasi-steady transient approach

An analytical model based on an assumption of combined quasi-steady and transient behavior of the process is presented to exemplify the unsteady, sphero-symmetric single droplet combustion under microgravity. The model used in the present study includes an alternative approach of describing the droplet combustion as a process where the diffusion of fuel vapor residing inside the region between the droplet surface and the flame interface experiences quasi-steadiness while the diffusion of oxidizer inside the region between the flame interface and the ambient surrounding experiences unsteadiness. The modeling approach especially focuses on predicting; the variations of droplet and flame diameters with burning time, the effect of vaporization enthalpy on burning behavior, the average burning rates and the effect of change in ambient oxygen concentration on flame structure. The modeling results are compared with a wide range of experimental data available in the literature. It is shown that this simplified quasi-steady transient approach towards droplet combustion yields behavior similar to the classical droplet theory.