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1.
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(p + 22), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(p +42). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.  相似文献   

2.
The 5-min oscillations in the photospheric velocity fields have been studied in detail from measurements on 14 absorption lines from three time sequences of spectrograms of high quality. The lines cover a range of heights in the solar atmosphere from log = + 0.2 to -1.2. Regions oscillating coherently are seen to have an average dimension of 8000 km and the oscillations in general last for 2 to 3 periods. The power spectrum analysis of high resolution enabled to determine the period of oscillation at each level very precisely. The period decreases with increase in height, being 304 s at the level log = + 0.2 and 295 s at the level log = -1.2. The low level lines possess considerable power in the low frequency range representing the convective overshoot from below. The oscillatory power increases with height, while the low frequency power decreases and the high frequency component remains substantially constant in the heights studied.The intensity fluctuations in the continuum, the line wing and core of Fe i 6358.695 have also been studied. The continuum power spectrum has practically all the power near the zero frequency range, with a very weak oscillatory component. The line wing intensity fluctuations resemble those in the continuum, whereas the line core clearly shows an oscillatory component similar to the velocity oscillations.  相似文献   

3.
A fraunhofer line profile depends on various parameters, partly related to the photospheric structure (T, P g, P e, v conv, v turb), partly to the atom or ion involved (such as oscillator strength, energy levels), partly also resulting from the interaction of the relevant kind of particles with the photosphere, and the photospheric radiation field. In this paper we shall mainly pay attention to the determination of: the macroturbulent (convective) velocities, v conv (); the damping constant (); the abundance, A el; the distribution function (v conv, ) of the convective velocities at each depth ; the source function, S (); the microturbulent velocities, v turb ().The particular difficulty with these unknowns is that they are, as a rule, coupled in the resulting line profiles, that is: the shapes and intensities in these profiles are determined by the combined influence of these unknowns (together with the other above-given parameters).In this paper we describe a method to determine these six unknowns empirically by separating them, in analysing accurate high-resolution observations of line profiles of a multiplet. The unknown functions and quantities are consecutively determined in the above given succession. For each determination another, appropriate part of the line profile is used. In some cases the influence of the mutual coupling of the various parameters cannot be completely eliminated, and an iterative method has to be used.The method is summarized in Table II and section 2, and is further explained in sections 3 to 8. It is applied to an infrared Ci multiplet. The main results are the following:  相似文献   

4.
The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ c+a{J 0()–J c} by Geovenelli, whereJ c is the total intensity at the continuum,J 0() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.  相似文献   

5.
This paper deals with a rather general class of magnetoatmospheres — media for which the restoring forces of buoyancy, compressibility and magnetic tension/pressure are important in sustaining wave motion. The magnetic field has the general form (B 0(z), 0,0) and there is also an aligned shear flow (U 0(z), 0, 0) present. After discussion of the equilibrium and stability of such systems, and certain mathematical properties of a particular system (an isothermal atmosphere with uniform magnetic field, of interest in solar physics), theory is developed which enables expressions to be written down for the mechanical wave energy flux associated with wave motion due to a transient source. These analytic expressions are very general and contain contributions from the continuous and discrete frequency spectra, corresponding respectively to freely propagating and trapped (or surface) waves. These fluxes are evaluated for various ranges of magnetic field, horizontal wavenumber, characteristic source times and frequency, for a simple constant-parameter atmosphere. The source is taken to be a transient fluctuation of the lower boundary, (modelling convective overshoot) which is taken to be located at the level 5000=0.08 in the solar atmosphere. The relative distribution of wave energy flux in the various modes is discussed in the context of solar physics parameters. The possible significance of leaky modes arising from supergranular or other flow, for the local flux balance in the solar chromosphere is outlined.  相似文献   

6.
A. Sauval 《Solar physics》1968,3(1):89-105
In order to obtain a better agreement between observed and computed values of the solar intensity, an improved temperature distribution is deduced for the range 0.02<0< 10. The intensity observations here considered refer to the wavelength region between 1980 and 129 500, and the center-limb variations generally go down to cos = 0.1. The improved model, given in Figure 4 and Table II, differs rather little from the Utrecht 1964 model, used here as a reference.It appears necessary to introduce an empirical correction function to be applied to the continuous absorption coefficient. This function was derived for the spectral region between 2000 and 130000 Å; it is shown in Figure 5.Furthermore, an extension of the model (1.10–7<0< 2.10–2) is deduced (see Table III and Figure 8), which reasonably well represents the observations of the ultraviolet solar flux ( 900–1700 Å).  相似文献   

7.
General integral transform of the exponential integralsE n is considered and will be denoted asB (k) n (). Different expressions and the equations satisfied byB (k) n are developed. Two-term recurrence formula forB (k) n (0) and three-term recurrence formula forB (k) n (); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy  相似文献   

8.
A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, 0=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb m(,,0) with Sobolev's function m(,0) playing the role of a source-function. Because the incident direction does not intervene, m is simply expressed as a single integral term involvingb m. For bottom illumination, an analogous equation holds for the other new functionh m(,,0). However, simple reciprocity relations link the two functions so that it is only necessary to considerb m; (ii) a transfer equation for the other new functiona m(,,,0) with a source-function provided by Sobolev's functionD m(,,0). For bottom illumination, another functionf m(,,,0) is introduced; by a similar argument using reciprocity relations,f m is reduced toa m rendering necessary only the consideration ofa m. However, a fundamental decomposition formula is obtained which shows thata m is expressible algebraically in terms of functions of a single angular variable. The functions m andD m are shown to be the values in the horizontal plane ofb m anda m, respectively. The other auxiliary functionsX m andY m are also expressed algebraically in terms ofb m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration.  相似文献   

9.
We consider the time-scale of orbital circularization for those massive binary systems that produce WR+C systems. Using the observation that such systems have acquired circular orbits on a time-scale of the order of the Main-Sequence lifetime of the initial secondary, we estimate the intrinsic time-scale of the tidal interaction 0. We find that the tidal dissipation in such systems is very efficient and that, on the average, 0 ~ 103 yr.  相似文献   

10.
Robert W. Noyes 《Solar physics》1985,100(1-2):385-396
The techniques and principal results of observational studies of stellar activity are summarized. Both chromospheric and coronal emission clearly track surface magnetic field properties, but it is not well known how the detailed relation between the emission and surface magnetic fields varies with spectral type. For lower Main-Sequence stars of the same spectral type, there is clear evidence of a close relationship between mean activity level and rotation period P rot. There is also less definitive evidence for a similar dependence on convective overturn time c , such that activity depends on the single parameter Ro = P rot/ c . For single stars, stellar rotation, and magnetic activity both decline smoothly with age. This implies a feedback between angular momentum loss rate and activity level. Temporal variations in mean stellar activity level mimic the solar cycle only for old stars like the Sun, being much more irregular for younger stars. The characteristic timescale of the variations (the cycle period) appears to depend on Ro for old stars, but shows no clear dependence on either rotation rate or spectral type for younger stars. Further data on mean activity and its variation for a large number of lower Main-Sequence stars should contribute significantly to our understanding of the causes of stellar magnetic activity.  相似文献   

11.
A simplified representation of the temperature distribution in the solar photosphere is proposed: ( 0) = 0 - 1 log 0. An expression is derived for the emergent continuous spectrum from the simple model. The limitations and applications of the simple model are discussed.  相似文献   

12.
We present a two-dimensional, nearly flux constant solar atmosphere which includes a physical model of granulation. If the inhomogeneous character of the solar photosphere is neglected in the construction of empirical models, the result is an underestimate of the temperature gradient in the layers below 0.5 and an overestimate of the convective flux penetration into the observable layers. The two-dimensional model adequately reproduces the mean limb darkening, the magnitude and center-to-limb variation of the intensity fluctuations, and the rms vertical and horizontal convective velocities.  相似文献   

13.
Semi-empirical models of solar faculae, cospatial with strong photospheric magnetic fields, have been constructed from continuum observations. The center-to-limb contrast of the various models was computed taking into account their geometrical shape. The adopted model whose horizontal size was taken to be 750 km, indicates that, in field regions, the temperature begins to rise outwards at z -125 km (above 5000 = 1) and that the extrapolated temperature at z -400 km is about 1500 K above that of the undisturbed atmosphere; the electron density is higher by a factor of about 30.  相似文献   

14.
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values i = i + i ,v i = i + v i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v 2 = 10–8) grow many times in marginally-stable state.  相似文献   

15.
The results of daily monitoring of the Ca K flux variations of integrated sunlight during the period 1 July 1979–18 February 1980 are presented, and the data analyzed by both power spectrum and autocorrelation methods. The latter method is found to be superior; in it the autocorrelation function is fit to a model having three parameters, viz. the maximum long-term autocorrelation c 1, the rotational period 0 and an effective lifetime 1. Values of c 1 = 0.26, 0 = 25.9 days, and 1 = 500 days are obtained for the Ca K flux ratio; somewhat different values of c 1 = 0.77, 0 = 28.0 days, and 1 = 89 days are obtained for the sunspot number for the same period. Rotational modulation is clearly evident for the relatively weak chromosphere of the Sun and should be even more easily observed for more active stars.  相似文献   

16.
Three different asymptotic branches of the two-fluid equations are found with e m , p n , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

17.
The paper describes a numerical experiment in which the effect of an assumed velocity distribution in the solar atmosphere on the intensity difference between a blue- and a red-wing filter-gram is derived. This results in the effective optical depth at which the velocity is measured. It is shown that this eff strongly depends on the assumed velocity distribution.  相似文献   

18.
With the help of a model atmosphere of the Sun we evaluate the pole-equator difference in flux (as measured by Dicke and Goldenberg) assuming the following type of pole-equator temperature difference (T=T e –T p ): (a) T 2K for > 0 (0 0.05); (b) T 10K for < 0.The small T at all optical depths given by (a) could, for example, be due to a pole-equator difference in effective temperatures. At small optical depths a difference in mechanical heating could give rise to the larger temperature difference given by (b). We compare the results of our calculations with Dicke and Goldenberg's observations.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

19.
Litvinenko  Yuri E. 《Solar physics》1998,180(1-2):393-396
Dimensional analysis is used to derive the distribution of solar flare energies,p() = A-3/2, in accordance with recent observational and numerical results. Several other scalings, notably fl 2 , where fl is the flare duration, are obtained as well.  相似文献   

20.
Twenty-seven typical binary systems have been investigated to study their power-output by gravitational radiation (P B ) and spiralling time (0) relation. It was found that these binary systems form two distinct groups. New relations have been given betweenP B and 0 for each group.  相似文献   

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