Poincaré's méthode nouvelle by skew composition

Poincaré designed the méthode nouvelle in order to build approximate integrals of Hamiltonians developed as series of a small parameter. Due to several critical deficiencies, however, the method has fallen into disuse in favor of techniques based on Lie transformations. The paper shows how to repair these shortcomings in order to give Poincaré’s méthode nouvelle the same functionality as the Lie transformations. This is done notably with two new operations over power series: a skew composition to expand series whose coefficients are themselves series, and a skew reversion to solve implicit vector equations involving power series. These operations generalize both Arbogast’s technique and Lagrange’s inversion formula to the fullest extent possible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Étude cinématique de la galaxie barrée NGC 5383

We present some observational results derived from plates taken with the nebular spectrograph at the 1.93-m telescope of the Observatoire de Haute Provence. The dispersion is 35 Å mm^?1 and the resolution is 85″ per mm. Radial velocities were measured at different points in the nucleus and in the bar. The nucleus is composed of two elements, of 5″ and 12″ diameter, inside a ring of radius 2 kpc. Radial velocities around the ring show a well-defined sinusoid with a maximum displaced about 15° from that predicted from the geometry of the outer parts of the galaxy. We can explain this displacement by a contraction velocity of 43 km s^?1. In the bar the kinematics is quite complex. The slit position (roughly aligned with the bar) was slightly different for each of the four plates taken. For those which bisect the nucleus the velocity field is symmetric, with a sharp discontinuity of 50 km s^?1 between the nucleus and the bar. The maximum velocity is not reached in our field of observation. Solid body rotation cannot be accepted. Spectra along the edge of the nucleus provides evidence for transverse motions in the bar of 100 km s^?1 at 4 kpc from the center. The rotation curve is drawn; in the hypothesis of a radial motion in the bar we have calculated the distribution of mass according to the method of Burbidge and Prendergast inside a 14 kpc radius; the mass is 10¹⁰ M _⊙. The iso-intensity tracings clearly show the presence of the two nuclear components, the absence of [Nii] emission on the north-west side of the bar and the absence of Hα in the south-west side. The ratio Hα/[Nii] between 2 and 5 at several spots indicates that Hii regions are highly excited in the nucleus and at the extreme end of the bar. The region of the bar where the ratio is less than 1 suggests high excitation by collision of energetic particle perhaps coming from the nucleus.     

Mesure des Raies de [Sii] dans Trois Nébuleuses planétaires de L'hémisphère Austral

Three southern planetary nebulae (NGC 2818, He 2-130, and NGC 3132) have been observed with the IDS (Image Dessector Scanner) combined with the Boller and Chivens spectrograph mounted at the Cassegrain focus of the 1.52 m telescope of the ESO in Chile. The spectrograph dispersion was 60 Å mm^–1 in the spectral range 6170–7298 Å. The slit aperture was 4×4. Spectra were obtained from an array of positions across each nebula along the E-W direction and/or N-S direction. The data reduction followed the standard IHAP routines for IDS observations. In order to derive electron density, only the [Sii] lines (6617 Å–6731 Å) are given in this paper. The results are in agreement with a shell structure for the observed nebulae.

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Toutes les observations ont été faites à l'Observatoire européen Austral (ESO) au Chili.     

Non-integrability of Hénon-Heiles system

We show that the Hénon-Heiles system with Hamiltonian H=\frac12(y₁²+y₂²)+\frac12(ax₁²+bx₂²)+\frac13dx₂³+cx₁²x₂{H=\frac12(y_1^2+y_2^2)+\frac12(ax_1^2+bx_2^2)+\frac13dx_2^3+cx_1^2x_2} is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or \frac dc=1, a=b; or \frac dc=6, a, b{\frac dc=1, a=b; {\rm or}\, \frac dc=6, a, b} arbitrary; or \frac dc=16, b=16a{\frac dc=16, b=16a}. Therefore, we get a complete classification of the Hénon-Heiles system in sense of integrability and non-integrability.     

Quelques résultats d'observation des spicules chromosphériques en K et D3

Résumé On étudie les spectres des spicules observés simultanément dans les raies K et D3 en fonction du temps et de l'altitude (2000<h<5000 km). Les mesures de la variation de l'intensité centrale I ₀ avec l'altitude, sont données dans le Tableau I. On donne des résultats comparatifs concernant l'énergie émise E _k et E _D3.La Figure 1 représente les variations de la largeur à mi-intensité des profils d'émission, (L) en fonction du temps et la Figure 2 en fonction de la hauteur.La classification des spicules en deux groupes: profil large (LW) et profil étroit (LN) a été confirmée. Il y a 2 fois plus de spicules LW que LN, la durée de vie des LN étant <2,5 min. Le Tableau II donne les valeurs moyennes de la largeur réduite L/.A l'aide des valeurs L, on détermine la microturbulence () dans les spicules en fonction de la hauteur (Figure 3, pour la raie K). La turbulence de la raie D3 est donnée dans un tableau dans le texte. Les résultats sont en bon accord. L'interprétation de ces résultats suggère que la microturbulence a deux composantes ₀ et _e. Pour les LN on a ₀ seul pour les LW on a ₀ + ₀, où ₀ est la turbulence au centre des spicules à l'endroit du champ magnétique fort (Figure 4a) et ₀ est la turbulence vers l'extérieur des spicules LW, là où le champ est faible (Figure 4b).

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We study in this paper the spectra of spicules on the solar limb observed simultaneously in the K and D3 lines in terms of time and altitude (2000<h<5000 km). The measures of the variation of the central intensity I ₀ with the altitude are given in Table I. We are also giving comparative results concerning the energy emitted E_K and E_D3 (Section 4).For different spicules, Figure 1 represents the variations of the total width at half intensity (L) of the emission profiles in terms of time and Figure 2 in terms of height.The classification of spicules in two groups: wide profile (LW) and narrow profile (LN) has been confirmed. There are approximately twice as many LW spicules as LN, the lifetime of LN spicules seems to be <2.5 min. Table II gives the average values of L/.With the help of L values, we can determine the microturbulence () in the spicules in function of the height (Figure 3, for the K line). The turbulence of the D3 line is given in a table in the text (Section 5.3). The results of both lines are concordant and the interpretation which we suggest (Section 5.4) is that the microturbulence has, generally speaking, two components ₀ and ₀. For the LN we have ₀ alone, and for the LW we have ₀ + _e, ₀ being the turbulence at the center of spicules where the magnetic field is strong (Figure 4a), whereas the _e is the turbulence towards the exterior of the LW spicules, where the magnetic field is weak (Figure 4b).

     

Observations planétaires a l'astrolabe

The Danjon astrolabe, first designed for the determination of time and latitude, has been used successfully for the improvement of star catalogues. From the very beginning of the sixities, it has also been used for planetary observations. From that time, systematic campaigns have been performed in various observatories and all major planets have been observed.The accuracy is of the same order of magnitude as that obtained with other instruments working in the field of positional astronomy. In this case, the instrument can contribute, by means of, meridian circles and astrographs to increase the available amount of observations for the purposes of celestial mechanics.Such observations for theories and ephemerides, issued from their improvements, would be of interest, the errors of the present ones being of the order-in some cases-of one arc-second, determined at the precision of a tenth of this value.Several improvements of the astrolabe have been taken into account such as the one which allows observations at different zenith distances. The length of arcs of trajectory for planets will increase and, with an adequate plate, it is now possible to observe the Sun. All the improvements, including a photoelectric device, will contribute to increasing the capability and the accuracy of the astrolabe, which is of interest in the field of planetary observations.Such a contribution, as well as those from the other classical instruments, will serve as a reference for the new technics such as radioastrometry, interferometry and space astrometry. This review paper must be considered as the contribution of the astrolabe to the various fields in which astrometry has to work at the present time.

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Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

Particle interactions with Alfvén solitons

We compute velocity and the corresponding energy changes due to non-resonant interactions of protons with Alfvén solitons. It is seen that the protons heat in the perpendicular direction but associated with this is a cooling in the parallel direction.ICTP (Trieste) Fellow under programme: Training and Research in Italian Laboratories.Instituto di Fisicia dello Spazio Interplanetario CNR, via G. Galilei, CP 27, 00044 Frascati, Italy.     

Coronal heating by Alfvén waves

Solar Physics - If Alfvén waves are responsible for the heating of the solar corona, what are the various dissipation processes, under what conditions are they important, and what...     

Alfvén waves in stellar winds

A mathematical model for undamped, toroidal, small-amplitude Alfvén waves in a spherically-symmetric or equatorial stellar wind is developed in this paper. The equations are reduced to a very simple form by using real Fourier amplitudes and the ratio of the inward and outward propagating wave amplitudes, which is interpreted as a measure of the relative influence of wave reflection in the flow, on the solution at a given point. Asymptotic solutions at large distances are found to depend only on one parameter, = / _P - the ratio of wave frequency and critical (or cutoff) frequency which is a flow characteristic; a = 1 divides solutions into two qualitatively different groups. When 1 the asymptotic (r-) ratio of the inward and outward propagating wave amplitudes does not depend on wave frequency and is equal to unity, while the phase shift between them changes; in this case the wave pattern is a standing wave. If > 1 the converse occurs with the ratio of the amplitudes decreasing rapidly as the frequency increases, and the phase shift equals to -1/2, corresponding to a propagating wave pattern. The result is also expressed in terms of velocity and magnetic field perturbations.Existence of a finite incoming wave amplitude solution at the Alfvén critical point indicates that this point is stable with respect to the perturbations which originate at the critical point and spend an infinite time in its vicinity.Special attention is paid to the applicability of the WKB approximation. It is argued that it can be used only in finite intervals which do not contain the Alfvén critical point, with inward propagating waves taken into account through the boundary conditions. It is shown that despite the presence of reflection, the outward propagating wave amplitude can be described reasonably well by the WKB formula, perhaps with different constants in different regions. In this context = 1 divides solutions which cannot be approximated by the WKB estimate at all at large distances (the first group), from those which can with any given accuracy.As an illustration of the analytical behaviour some numerical results are shown using a cool wind model. These are likely to express qualitatively the features of the Alfvén waves in any stellar wind, since the only assumptions about the flow used in the analytical study of the wave equations were that: the flow has small velocity at the base of the corona; it then passes through the critical point, and reaches its finite non-zero limit at infinity.     

Interchange Reconnection Alfvén Wave Generation

Given recent observational results of interchange reconnection processes in the solar corona and the theoretical development of the S-Web model for the slow solar wind, we extend the analysis of the 3D MHD simulation of interchange reconnection by Edmondson et al. (Astrophys. J. 707, 1427, 2009). Specifically, we analyze the consequences of the dynamic streamer-belt jump that corresponds to flux opening by interchange reconnection. Information about the magnetic field restructuring by interchange reconnection is carried throughout the system by Alfvén waves propagating away from the reconnection region, distributing the shear and twist imparted by the driving flows, including shedding the injected stress-energy and accumulated magnetic helicity along newly open fieldlines. We quantify the properties of the reconnection-generated wave activity in the simulation. There is a localized high-frequency component associated with the current sheet/reconnection site and an extended low-frequency component associated with the large-scale torsional Alfvén wave generated from the interchange reconnection field restructuring. The characteristic wavelengths of the torsional Alfvén wave reflect the spatial size of the energized bipolar flux region. Lastly, we discuss avenues of future research by modeling these interchange reconnection-driven waves and investigating their observational signatures.     

Fip Enhancement by Alfvén Ionization

Alfvén ionization is offered as a possible mechanism underlying the enhanced population of low first ionization potential (FIP) species in the solar corona. In this process, the photospheric flow impinging on the magnetic structure of a coronal flux tube collides with, and displaces, ions in the magnetised plasma within the flux tube. This leads to pockets of charge imbalance that persist due to the impeded electron transport perpendicular to the magnetic field. The localised electric field then energises electrons to the impact ionization energy threshold of low-FIP components in the surface flow. Such species remain trapped in the plasma, and drift up the magnetic structure, causing a localised population enhancement compared to photospheric levels. We find that this mechanism successfully accounts for observed biases for flow speeds known to exist in the photosphere, and moreover explains certain anomalous abundances which do not fit into existing theories.     

Coronal loop heating by Alfvén waves

The excitation and dissipation of global and surface Alfvén waves and their conversion into kinetic Alfvén waves have been analyzed for solar coronal loops using a cylindrical model of a magnetized plasma. Also the optimal conditions for coronal loop heating regimes with density of dissipated power 10³ erg cm^–3 s^–1 by the new scheme named combined Alfvén wave resonance are found. Combined Alfvén wave heating regime appears when the global Alfvén wave is immersed into the Alfvén continuum with the condition of not-so-sharp distribution of axial current.Instituto de Matemática, Universidade Federal Fluminense, Niterói, RJ, Brazil     

Alfvén waves in the solar atmosphere

The linearized propagation of axisymmetric twists on axisymmetric vertical flux tubes is considered. Models corresponding to both open (coronal hole) and closed (active region loops) flux tubes are examined. Principal conclusions are: Open flux tubes: (1) With some reservations, the model can account for long-period (T 1 hr) energy fluxes which are sufficient to drive solar wind streams. (2) The waves are predicted to exert ponderomotive forces on the chromosphere which are large enough to alter hydrostatic equilibrium or to drive upward flows. Spicules may be a consequence of these forces. (3) Higher frequency waves (10 s T few min) are predicted to carry energy fluxes which are adequate to heat the chromosphere and corona. Nonlinear mechanisms may provide the damping. Closed flux tubes: (1) Long-period (T 1 hr) twists do not appear to be energetically capable of providing the required heating of active regions. (2) Loop resonances are found to occur as a result of waves being stored in the corona via reflections at the transition zones. The loop resonances act much in the manner of antireflectance coatings on camera lenses, and allow large energy fluxes to enter the coronal loops. The resonances may also be able to account for the observed fact that longer coronal loops require smaller energy flux densities entering them from below. (3) The waves exert large upward and downward forces on the chromosphere and corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Sur les mouvements réguliers des satellites

Résumé Il est envisagé dans ce travail le problème du mouvement translatoire-rotatoire d'un corps solide invariable dans le champ centrale de la gravitation Newtonienne. Il est établie auparavaat la forme générale du développement de la fonction des forces du problème et il est marqué ses propriétés remarquables. Nous abordons ensuite l'étude des mouvements, nommés reguliers, dans lesquels le centre des masses du corps décrit une orbite circulaire Keplerienne, tandis que le corps lui-même conserve une orientation invariable par rapport à cette orbite.Il est démontré, que ces mouvements peut admettre seulement le corps possedant la symétrie axiale dynamique. Nous distinguons les trois types différents des mouvements réguliers, dont nous nommons par flotte, flèche et rais.Il existenr encore quelques cas intermédiaires.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Quantum treatment of kinetic Alfvén wave

Dispersion properties of kinetic Alfvén wave in quantum magnetoplasma are derived. The quantum contribution to the Landau damping of kinetic Alfvén wave is also derived by using linearized Vlasov equation which contains the Bohm quantum potential. Classical Landau damped kinetic Alfvén waves play an important role in turbulence of astrophysical plasmas. The quantum modification in Landau damping of kinetic Alfvén wave can also play a significant role in changing the scaling law of turbulent spectra as well as the formation of damped localized Alfvénic structures in dense astrophysical plasmas.     

Modulational instability of finite-amplitude Alfvén waves

It is shown that a recent conclusion of Shivamaggi that the modulational instability of finite amplitude Alfvén waves arises when the density cavity travels at subsonic speeds, is incorrect.     

Alfvén waves and the sunspot phenomenon

Parker's explanation of the sunspot phenomenon in terms of the enhanced emission of Alfvén waves (solar vulcanology) is shown to be compatible with observation only if 90% of the waves propagate downwards. Further difficulties arise if the region of cooling by Alfvén wave generation is restricted to a depth of 2 Mm. However, it is shown that, if Alfvén wave generation is included in a recent model proposed by Meyer, Schmidt, Weiss and Wilson, these difficulties may be resolved. The problem of the sharp umbra and penumbra boundaries is discussed and it is shown that features of this combined model are relevant to the flare phenomenon.     

Statistical Properties of Alfvén Ion Cyclotron Waves and Kinetic Alfvén Waves in the Inner Heliosphere

Alfvén ion cyclotron waves(ACWs) and kinetic Alfvén waves(KAWs) are found to exist at <0.3 au observed by Parker Solar Probe in Alfvénic slow solar winds. To examine the statistical properties of the background parameters for ACWs and KAWs and related wave disturbances, both wave events observed by Parker Solar Probe are selected and analyzed. The results show that there are obvious differences in the background and disturbance parameters between ACWs and KAWs. ACW events have a relatively hi...