A theory is presented for the calculation of continuous absorption due to far wing contributions allowed lines. The based on quasistatic approximation limit and binary collision one absorber molecule bath molecule. In line space, motion dipole moment molecule, determined by time displacement Liouville operator related total Hamiltonian approximately expressed as ordered product two operators, intermolecular potential other unperturbed Hamiltonian. Using a Laplace transformation, spectral...

The far wing line shape theory developed previously and applied to the calculation of continuum absorption pure water vapor is extended foreign-broadened continua. Explicit results are given for H2O–N2 H2O–CO2 in frequency range from 0 10 000 cm−1. based on quasistatic binary collision approximations assumes interaction potential an isotropic Lennard-Jones part leading anisotropic multipolar (dipole–quadrupole) term. For H2O–N2, positive negative resonant average functions coefficients...

A method is presented for the calculation of tight upper and lower bounds energy eigenvalues Schr\"odinger equation. The based on a rational functional approximation series expansion solution Riccati equation logarithmic derivative wave function. Specific applications one-dimensional anharmonic oscillators Yukawa potential are given, present results compared with those obtainable by other procedures.

A theory is presented for the calculation of continuous absorption water molecules in millimeter spectral region. The based on a generalization Fano’s which density, Fourier transform dipole-moment correlation function, calculated system consisting pair molecules. internal states are written terms line space system, and resolvent operator obtained using well-known Lanczos algorithm. For interaction between two molecules, we include only leading dipole–dipole term long-range anisotropic...

A far wing line shape theory based on the binary collision and quasistatic approximations that is applicable for both low high frequency wings of vibration–rotational bands presented. This applied in order to calculate temperature dependence continuous absorption coefficient frequencies up 10 000 cm−1 pure water vapor. The calculations are made assuming an interaction potential consisting isotropic Lennard-Jones part with two parameters consistent values obtained from virial data anisotropic...

The statistical theory proposed by Rosenkranz to calculate the continuous absorption water molecules in high-frequency (infrared) wing of pure rotational band is reviewed and extended. In review there a discussion, particular, approximations that are made, including those necessary which limit applicability other spectral regions, made for calculational convenience. Then, several extensions discussed, increasing number states used band-average relaxation parameter, modifying definition this...

A method described previously for obtaining upper and lower bounds the eigenenergies of Schr\"odinger equation parity-invariant central potentials is extended applied to asymmetric one-dimensional potentials. The procedure consists transforming into a Ricati one logarithmic derivative wave function. solution latter approached by series Pad\'e approximants. Approximate are obtained from roots associated determinants, such proved, in some cases, be or actual eigenenergies. illustrated...

A comprehensive investigation concerning the intrinsic properties of chaotic Rulkov neuron model is carried out by analyzing three distinct types two-dimensional parameter-plane diagrams. The first type diagram, established qualitative analysis combined with center manifold theorem and normal form theory, systematically characterizes clearly fixed point possible bifurcation curves. second generated numerically, visually delineates stability domains for periodic solutions, quasi-periodic...

We investigated the magnitude and temperature dependence (T dependence) of dimer absorption in region 0-600 cm(-1) collision-induced (CIA) 0-1150 cm(-1). Together with our previous study self water-vapor continuum contributions resulting from far-wing line shapes allowed H(2)O lines infrared window between 800 1150 cm(-1), we find that three mechanisms have completely different T behaviors. The has strongest negative far wings a moderately strong one. Meanwhile, CIA exhibits mild dependence....

A far-wing line shape theory based on the binary collision and quasistatic approximations that is applicable for both low- high-frequency wings of vibration-rotational bands has been developed. This applied in order to calculate frequency temperature dependence continuous absorption coefficient frequencies up 10,000 cm−1 pure H2O H2ON2 mixtures. The calculations were made assuming an interaction potential consisting isotropic Lennard-Jones part with two parameters are consistent values...

The water vapor foreign-continuum absorption has been calculated theoretically from first principles for the millimeter wave spectral region as a function of frequency f and temperature T. calculations are made using Lanczos algorithm by writing resolvent operator (ω−L)−1 continued fractions. In order to guarantee quick convergence fractions, line space H2O is divided into two subspaces: one consists positive resonance lines other negative ones. By ignoring coupling between them, expressed...

With different choices of the cut-offs used in theoretical calculations, we have carried out extensive numerical calculations N2-broadend Lorentzian half-widths H2O lines using modified Robert–Bonamy formalism. Based on these results, are able to thoroughly check for convergence. We find that, with low-order commonly literature, one is obtain converged values only large half-widths. Conversely, small half-widths, much higher necessary guarantee also analyse uncertainties associated...

Absolute absorption rates of pure water vapor and mixtures nitrogen have been measured in the atmospheric window at 239 GHz. The dependence on pressure as well temperature has obtained. experimental data are compared with several theoretical or empirical models, satisfactory agreement is obtained models involving a continuum; case vapor, continuum contribution based upon recent developments gives good results. stronger than that proposed commonly used transmission model.

Starting from the well-known expression between absorption coefficient and spectral density F(ω), Fourier transform of dipole correlation function, we use a projection operator to average out degrees freedom bath variables. As result, F(ω) can be written in terms memory function effects due initial correlations, all which are confined line space absorber molecule. The correlations influence form necessary order satisfy principle detailed balance. There is relationship existence sum rules...

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this contains several approximations whose applicability not thoroughly justified. One of them is that lines interest are well isolated. When these authors formalism, they have relied on assumption twice. First, spectral density F(ω), only considered diagonal matrix elements relaxation operator. Due to...

A far-wing line shape theory in which the validity of detailed balance principle is maintained each step derivation presented. The role total density matrix including initial correlations analyzed rigorously. By factoring out rapidly varying terms complex-time development operator interaction representation, better approximate expressions can be obtained. As a result, spectral density, Fourier transform dipole correlation function, expressed line-coupling functions two coupled lines are...

The far-wing line shape theory within the binary collision and quasistatic framework developed previously for linear molecules using coordinate representation has been generalized to symmetric- asymmetric-top molecular systems. However, due more variables needed specify orientation of these complicated molecules, one evaluate multidimensional integrals with higher dimensionality this would be intractable practical calculations. In cases where anisotropic interaction contains cyclic...