Exact solutions in the FPU oscillator chain

The potential of employing nitric oxide (NO) as a spectrometric probe to monitor the evolution of free electrons is explored in this article for conditions occurring during the propagation of a positive streamer in atmospheric pressure nitrogen. An extension of the spectroscopic approach, based on a comparison of the relative emission intensity of electronic states with different excitation thresholds is proposed, considering typical space and timescales of streamers. Basic characteristics of electron-impact excitation processes are evaluated for N2(X?1?g+), N2(C?3?u) and NO(A?2?+) electronic states utilizing recently published cross section data. Emission of the N2 second positive (2.PG) and NO-? systems is inspected by means of a simple collisional-radiative model considering energetic Maxwellian electrons as the primary excitation source of involved electronic states. A simple tool for evaluating `spectroscopic Maxwellian electron temperature' from relative intensities of the N2 2.PG and NO-? systems emissions is provided.

https://iopscience.iop.org/article/10.1088/0022-3727/35/16/311/pdf

The modelling of streamer-induced emission in atmospheric pressure, pulsed positive corona discharge: N2 second positive and NO-γ systems

New spectrographic observations of the Earth's dayglow have been acquired by the Arizona Airglow Experiment (GLO) flown on the space shuttle. GLO is an imaging spectrograph that records simultaneous vertical profiles of prominent Earth limb emissions occurring at wavelengths between 115 and 900 nm. This study addresses the measured emissions from the N2 triplet states (first positive, second positive, and Vegard-Kaplan band systems) and their excitation by the local photoelectron flux. The triplet state population distributions modeled for aurora by Cartwright [1978] are modified for dayglow conditions by changing to a photoelectron-flux energy distribution and including resonance scattering by the first positive system. Modeled and observed intensities are in excellent agreement, in contrast to the well-studied auroral case. This work concentrates on dayglow conditions at 200 km altitude near the subsolar point. Parameters to infer the local photoelectron flux from the emission band intensities are provided. Several atomic oxygen dayglow emission features were analyzed to complement the N2 analysis. The photoelectron-excited O I(135.6, 777.4 nm) lines were found to be 3 to 4 times weaker than predicted while the O I(630.0, 844.6 nm) lines were in close agreement with the model prediction.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JA00771

N2 triplet band systems and atomic oxygen in the dayglow

Differential cross sections for electron impact excitation of the optically forbidden C 3Piu, E 3Sigmag+ and a" 1Sigmag+ states of N2 have been measured at incident energies of 17.5 and 20 eV and over the angular range 10 to 100 degrees . Cross sections for vibrational and electronic transitions have been obtained. Integral electronic cross sections for the C 3Piu and E 3Sigmag+ states have also been determined. The present results are compared with previous experimental and theoretical studies.

Differential cross sections for electron impact excitation of the C 3Piu, E 3Sigmag+ and a" 1Sigmag+ states of N2

We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape toward the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four different cases depending on the perturbation function which controls the number of escape channels on the configuration space. In every case, we computed extensive samples of orbits in both the configuration and the phase space by numerically integrating the equations of motion as well as the variational equations. It was found that in all examined cases, regions of non-escaping motion coexist with several basins of escape. The larger escape periods have been measured for orbits with initial conditions in the vicinity of the fractal structure, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. In addition, we related the model potential with applications in the field of reactive multichannel scattering. We hope that our numerical analysis will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.

Escapes in Hamiltonian systems with multiple exit channels: part II

Ergodic components in the stochastic region in a Hamiltonian system

In order to classify fully developed chaos produced by simple one-dimensional maps the Pearson walk which is a special kind of two-dimensional random walk is introduced to visualize, in principle, all the orbits starting from different initial points in one diagram. Chaos of the tent map, standard baker transformation and the logistic map is clearly distinguished from one another in our Pearson-walk representation, which also provides information on not-fully developed chaos that emerges for smaller parameter values for each map. In the present visualization it is also clearly seen how characteristics of the so-called window is differentiated from those of the purely periodic region in the logistic map.

Pearson-walk visualization of the one-dimensional chaos

It is shown that the induction phenomenon in the exchange of energies of normal modes found by computer experiments is an inherent property of the anharmonic lattice vibration and its behavior obeys the time reversal even after the elapse of the induction period. The instability of the normal modes when one mode is excited initially is related to the induction phenomenon, and is discussed by the application of the instability region of the Mathieu function. The exponential orbital separation is also shown to take place after the elapse of the induction period. This guarantees the C-property of the anharmonic lattice vibration.

The Induction Phenomenon and Ergodicity in the Anharmonic Lattice Vibration

Validity of the Franck-Condon approximation is experimentally examined for electron-impact excitation of the C 3 ∏ u state of N 2 molecule. The relative excitation cross-sections for associated vibrational levels up to υ=4 at an electron energy of 48 eV are derived with measuring the emission band intensities of the second positive system. The result is compared with the prediction by the approximation, and appreciable discrepancies are found between them. In particular, the ratio σ υ=3 /σ υ=0 of the cross-sections obtained is by about a factor of two larger than the corresponding ratio of the Franck-Condon factors.

Vibrational-Level Distribution in Electron-Impact Excitation of the N2 C3∏u State: Its Disagreement with the Franck-Condon Approximation

Computer calculations on a classical dynamical system of two degrees of freedom with the hamiltonian, \(H_{\varepsilon}=\frac{1}{2}(p_{1}^{2}+p_{2}^{2})+\frac{1}{2}(q_{1}^{2}+q_{2}^{2})+q_{1}^{2}q_{2}+\frac{1}{3}(1-2\varepsilon)q_{2}^{3}\) are presented. The Poincare mapping on ( q 2 , p 2 ) plane of this system around e =0.5 revealed that there exist several ergodic components in the stochastic region, and furthermore they have a hierarchy structure. The Lyapunov characteristic numbers are also shown to have different values for different ergodic components.

Atsushi Ichimura

Papers

Ergodic components in the stochastic region in a Hamiltonian system

Pearson-walk visualization of the one-dimensional chaos

The Induction Phenomenon and Ergodicity in the Anharmonic Lattice Vibration

Vibrational-Level Distribution in Electron-Impact Excitation of the N2 C3∏u State: Its Disagreement with the Franck-Condon Approximation

On the Stability of Isolating Integrals. II. Ergodic Components in the Stochastic Region