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1.
We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section by the points (1)O(0,0), (2)C 1,C 2(±y c, 0), (3)B 1,B 2(O,±1) and (4) the boundary . The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of are given by simple approximate formulae. At every transitionS U a set of 4 asymptotic curves is formed atO. For larger the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC 1,C 2 at infinite heteroclinic points. At every transitionU S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB 1,B 2. We find indications that the number of spiral rotations tends to infinity as . Therefore new tangencies between the asymptotic curves appear for arbitrarily large . As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large .  相似文献   

2.
A unified picture of the photodissociation of theC 2 H radical has been developed using the results from the latest experimental and theoretical work. This picture shows that a variety of electronic states ofC 2 are formed during the photodissociation of theC 2 H radical even if photoexcitation accesses only one excited state. This is because the excited states have many avoided corssings and near intersections where two electronic states come very close to one another. At these avoided crossings and near intersections, the excited radical can hop from one electronic state to another and access new final electronic states of theC 2 radical. The complexity of the excited state surfaces also explains the bimodal rotational distributions that are observed in all of the electronic states studied. The excited states that dissociate through a direct path are limited by dynamics to produceC 2 fragments with a modest amount of rotational energy, whereas those that dissociate by a more complex path have a greater chance to access all of phase space and produce fragments with higher rotational excitation. Finally, the theoretical transition moments and potential energy curves have been used to provide a better estimate of the photochemical lifetimes in comets of the different excited states of theC 2 H radical. The photochemically active states are the 22+, 22II, 32II, and 32+, with photodissociation rate constants of 1.0×10–6, 4.0×10–6, 0.7×10–6, and 1.3×10–6s–1, respectively. These rate constants lead to a total photochemical lifetime of 1.4×105 s.  相似文献   

3.
W. Dziembowski 《Solar physics》1983,82(1-2):259-266
It is shown that in consequence of the parametric resonance, g modes of low spherical harmonic degree l are strongly coupled to the modes of high degree. The coupling limits the growth of low l modes to very small amplitudes. For g 1, l = 1 mode, the final amplitude of the radial velocity is of the order of 10 cm s-1. A mixing of solar core as a result of a finite-amplitude development of linear instability of this mode is thus highly unlikely.  相似文献   

4.
We distinguish between regular orbits, that bifurcate from the main families of periodic orbits (those that exist also in the unperturbed case) and irregular periodic orbits, that are independent of the above. The genuine irregular families cannot be made to join the regular families by changing some parameters. We present evidence that all irregular families appear inside lobes formed by the asymptotic curves of the unstable periodic orbits. We study in particular a dynamical system of two degrees of freedom, that is symmetric with respect to the x-axis, and has also a triple resonance in its unperturbed form. The distribution of the periodic orbits (points on a Poincaré surface of section) shows some conspicuous lines composed of points of different multiplicities. The regular periodic orbits along these lines belong to Farey trees. But there are also lines composed mainly of irregular orbits. These are images of the x-axis in the map defined on the Poincaré surface of section. Higher order iterations of this map , close to the unstable triple periodic orbit, produce lines that are close to the asymptotic curves of this unstable orbit. The homoclinic tangle, formed by these asymptotic curves, contains many regular orbits, that were generated by bifurcation from the central orbit, but were trapped inside the tangle as the perturbation increased. We found some stable periodic orbits inside the homoclinic tangle, both regular and irregular. This proves that the homoclinic tangle is not completely chaotic, but contains gaps (islands of stability) filled with KAM curves.  相似文献   

5.
The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (102–104 M ⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.  相似文献   

6.
We study the distribution of regular and irregular periodic orbits on a Poincaré surface of section of a simple Hamiltonian system of 2 degrees of freedom. We explain the appearance of many lines of periodic orbits that form Farey trees. There are also lines that are very close to the asymptotic curves of the unstable periodic orbits. Some regular orbits, sometimes stable, are found inside the homoclinic tangle. We explain this phenomenon, which shows that the homoclinic tangle does not cover the whole area around an unstable orbit, but has gaps. Inside the lobes only irregular orbits appear, and some of them are stable. We conjecture that the opposite is also true, i.e. all irregular orbits are inside lobes.  相似文献   

7.
In this paper, new trigonometric series representations of the orbital inclination functionF imp (i) in multiples of cosines or sines will be established for all possible values ofl, m, andp. For such representations, the literal analytical expressions and the recurrence formulae satisfied by their coefficients will be established. Moreover, an economic algorithm for the table formulation of these coefficients for the possible values ofl, m, andp is given. Finally, numerical examples of the representations forl=2(1)4;m=0(1)l;p=0(1)l are also included.  相似文献   

8.
The increasing central concentration of the Sun with age modifies the acoustic eigenfrequencies. In particular, the frequency separation d l =3(2l+3)–1v n,l –v n–1,l+2 for modes with l + 1/2 n decreases as nuclear reactions augment the molecular-weight gradient in the energy-generating core. If, for example, the Sun were older than is generally believed, one might therefore expect d l to be smaller than current theoretical predictions. On the other hand, to ensure that the luminosity is consistent with observations, the presumed initial hydrogen abundance would need to be enhanced, thereby reducing the resultant molecular-weight gradient. Thus there is some degree of cancellation of the two major factors that determine d l .Various authors have either reported directly on the sensitivity of d l , or have provided the information from which it can be calculated. We have added our own computations. There is broad agreement amongst the results: d l diminishes with the presumed age of the Sun at the rate of about 1 Hz per Gy for l = 0; the magnitude of the rate appears to decline with increasing l.  相似文献   

9.
We measure the 2-1 cumulant correlator power spectrum, a degenerate three-point statistic or integrated bispectrum, from the WMAP first and three year data releases (WMAP1 and WMAP2, respectively). We present a method of estimating these statistics using the pseudo-Cl-based SpICE estimator. We interpret the measurements in a maximum likelihood framework using theoretical predictions based on the simplest fNL model. All calculations are repeated on Monte Carlo simulations to obtain covariance matrices of our measurements. Application of the theory of random matrices revealed that the experimental covariances are consistent with a random matrix approximation. Finally, our χ2 analysis yields fNL = 22 ± 52(1σ) from WMAP2.  相似文献   

10.
Based on an analysis of the VLBI observations performed in 1985?C2010 within the framework of international geodetic programs on global networks of stations, we have obtained statistically significant corrections to the parameters of lunisolar tides??the nominal complex Love/Shida numbers. The new integral (frequency-independent) values of these parameters (in 10?4) are h (0) = (6113 ± 3) ? (33 ± 2)i, l (0) = (843 ± 1) ? (5 ± 2)i for a total tide; h (0) = (6106 ± 3) ? (10 ± 6)i, l (0) = (843 ± 1) ? (8 ± 1)i for diurnal tides; and h (0) = (6106 ± 3) ? (24 ± 3)i, l (0) = (843 ± 1) + (3 ± 1)i for semi-diurnal tides. We have detected a new effect of asymmetry in the horizontal tidal displacements in the direction of tectonic motions for 50 VLBI stations. We have determined upper limits for the influence of the frequency-dependent resonance effects whose estimation accuracy is limited by an abundance of close frequencies in their harmonic expansion. The influence of the transfer function for tides on the VLBI observations has turned out to be lower than the measurement accuracy. In future, positional GPS/GLONASS measurements are planned to be used to refine the resonance effects and the transfer function.  相似文献   

11.
The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A1 regions for oblate larger primary, A 1 beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A 1values.  相似文献   

12.
For the equation describing plane oscillations and rotations of a satellite, we consider families of symmetric generalized periodic solutions with integral rotation number p. We give new confirmations of the hypothesis: there are only four classes of these families with topologically different structures, namely, the classes of families of periodic solutions with p≥ 1, p= 0, p=−1, and p≤−2. Besides, we demonstrate that the vertices of cusps of these families are placed on some analytical curves, and the same is true for the multiple intersections of these families with other families.  相似文献   

13.
We report multi-frequency radio continuum and hydrogen radio recombination line observations of HII regions near l = 24.8°, b = 0.1° using the Giant Metrewave Radio Telescope (GMRT) at 1.28 GHz (n = 172), 0.61 GHz (n = 220) and the Very Large Array (VLA) at 1.42 GHz (n = 166). The region consists of a large number of resolved HII regions and a few compact HII regions as seen in our continuum maps, many of which have associated infrared (IR) point sources. The largest HII region at l = 24.83° and b = 0.1° is a few arcmins in size and has a shell-type morphology. It is a massive HII region enclosing ∼550 M⊙ with a linear size of 7 pc and an rms electron density of ∼110 cm−3 at a kinematic distance of 6 kpc. The required ionization can be provided by a single star of spectral type O5.5. We also report detection of hydrogen recombination lines from the HII region at l = 24.83° and b = 0.1° at all observed frequencies near V lsr = 100 km s−1. We model the observed integrated line flux density as arising in the diffuse HII region and find that the best fitting model has an electron density comparable to that derived from the continuum. We also report detection of hydrogen recombination lines from two other HII regions in the field.  相似文献   

14.
It is known that the correlation between the observed visible luminositym(z), angular dimension (z) of galaxies on the red shiftz and theoretical relations of the standard cosmology is possible only under the assumption that the luminosity and object dimension evolution are equal toL(z) =L 0(z + 1)3.2 andl(z) =l 0(z + 1)–2, respectively. This evolution is hypothetical, since it is defined by a theory which is not confirmed by experience. In order to solve the problem on the reality of the Universe expansion, it is sufficient to prove or disprove these conclusions using methods of measurement independent of the theory. One of these methods consists of defining the dependence of the radiation spectra of galaxies and quasars onz which evidently is proportional to the spectrum of absolute luminosityL(, z). It has subsequently been shown that the spectrum form is practically independent of the red shift - i.e., it remains constant during the lifetime of galaxies and quasars. Consequently, to explain the luminosity increase required by the standard cosmology, it is necessary to admit a completely unreal entity (at all wavelengths of the optical spectrum increase) of the radiation spectral density of (z + 1)3.2 times. We can conclude that in reality the luminosity evolution is either absent or its power index is smaller at least by an order of magnitude. It is likely, therefore, that the established is the result of an inadequate standard in cosmology.Another method is the use of the observed relations between the parameters ofL andl galaxies. A number of measurements made by different authors gives the relationlL a , where 0.33a1.6. It then follows thatl(z)(z + 1)3.2a . This dependence of the galaxy dimension is inverse to the dependence predicted by the standard cosmology. Besides, in order to make a correlation between thel(z)(z + 1)3.2a and measurements of (z), it is necessary that indices of the degree of luminosity evolution should be smaller by an order of magnitude.Thus, the luminosity increase and simultaneous decrease of galaxy and quasar dimensions predicted by the standard cosmolog are not confirmed by the direct astrophysical measurements. This discrepancy is the consequence of an incorrect hypothesis of Universe expansion and the relativistic cosmology based on it.  相似文献   

15.
We present evidence for Ly pumping of the Lyman band system of molecular hydrogen in Herbig-Haro 7 and the bipolar outflow DR 21. For this study we have measured several vibrational-rotational emission lines of H2 whose energy levels are widely spaced and ranging from 6000 (v = 1) to 25000 Kelvin (v = 4). We show that the near-infrared H2 emission from the shocked gas in HH 7 can be well described by a bow C-type shock. The enhanced emission observed from the higher energy levels (v > 3) can be well modelled by employing the Ly pumping mechanism.In the DR 21 outflow the multi-line study showed that different physical conditions exist in the eastern and western emission lobes. The higher H2 line ratios measured in the eastern lobe suggests a higher Ly pump rate which may be locally produced in the fast bowshocks. The FUV radiation field emanating from the central HII regions may in addition be exciting the Lyman and Werner bands of H2 in the molecular lobes.We show that the observed H2 emission can be interpreted in terms of a simple model consisting of a C-type bowshock, which produces the low excitation H2 emission, and a FUV radiation field with enough Ly line radiation to produce the high excitation H2 emission through fluorescence.  相似文献   

16.
The sunspot occurrence probability defined in Paper I is used to determine the Legendre-Fourier (LF) terms in the rate of emergence of toroidal magnetic flux,Q(, t), above the photosphere per unit latitude interval, per unit time. Assuming that the magnetic flux tubes whose emergence yields solar activity are produced by interference of global MHD waves in the Sun, we determine how the amplitudes and phases of the LF terms in the toroidal magnetic fieldB , representing the waves, will be related to those of the LF terms inQ(, t). The set of LF terms in Q that represents the set of waves whose interference produces most of the observed sunspot activity is {l = 1, 3, , 13;v =nv *,n = 1, 3, 5}, wherev * = 1/21.4 yr–1. However, among the shapes of sunspot cycles modeled using various sets of the computed LF terms the best agreement with the observed shape, for each cycle, is given by the set {l = 3 orl = 3, 5; andn = 1, 3 orn = 1, 3, 5}. The sets of terms: {l = 1, 3, 5, 7;n = 1}, {l = 1, 3, 5, 7;n = 3}, {l = 9, 11, 13, 15;n = 1} and {l = 9, 11, 13, 15;n = 3} seem to represent four modes of global MHD oscillation. Correlations between the amplitudes (and phases) of LF terms in different modes suggest possible existence of cascade of energy from constituent MHD waves of lowerl andn to those of higherl andn. The spectrum of the MHD waves trapped in the Sun may be maintained by the combined effect of this energy cascade and the loss of energy in the form of the emerging flux tubes. The primary energy input into the spectrum may be occurring in the mode {l = 1, 3, 5, 7;n = 1). As expected from the above phenomenological model, the size of a sunspot cycle and its excess over the previous cycle are well correlated (e.g., 90%) to the phase-changes of the two most dominant oscillation modes during the previous one or two cycles. These correlations may provide a physical basis to forecast the cycle sizes.  相似文献   

17.
We consider bifurcation of 3D periodic orbits from the plane ofmotion of the primaries in the photogravitational restricted three-bodyproblem. The simplest periodic 3D orbits branch from the plane periodicorbits of indifferent vertical stability. We compute the first few suchorbits of the basic families l, m, i, h, a, b, c forvarying mass parameter and for varying radiation coefficient of thelarger primary. The horizontal stability of the orbits is also computedleading to predictions about possible stability of the 3D orbits.  相似文献   

18.
We test for age and metallicity gradients in the Galactic Bulgebetween the two low extinction windows Baade's window (l = 1° .1b=−4° .8) and Sagittarius-I (l=1° .3 b=−2° .7). We derive ametallicity difference of ≤ 0.2 dex between BW andSGR-I window. This corresponds to a metallicity gradient of 1.3 dexkpc-1. This steep gradient is reconcilable with the existence of ashort scale length inner component to the Bulge, most likely thatprominent in the NIR, which perhaps forms a separate entitysuperimposed on the larger, optical Bulge. Through number counts incolour-magnitude diagram around the turnoff for several fields andclusters, extending over a range in galactic longitude we find no evidencefor a significant young stellar population in the GalacticBulge. Previous suggestions of the existence of a significant youngstellar population have most likely incorrectly identified theforeground disk stars. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

19.
The coherent 5-min photospheric pressure oscillations with spherical harmonic degrees in the range 100 <l< 1000 were directly imaged over the photosphere with the monochromatic solar telescope FPSS at Meudon Observatory. Movie films were obtained with images spatially filtered to select sizes of increasing wave numbers (or l). Areas with ephemeral concentrations of coherent waves evolve in shape and may move horizontally with velocities of several tenths of km s–1. When a large number of waves are interacting, the maximum vertical velocity V max of the pulsation reaches around 1000 m s–1, irrespective of the size. Extrapolation to the ideal case of a single isolated wave gives V max proportional to size. For the areas of the smallest scale measured (l = 1000), when about 100 waves are interacting, V max is found to be 260 + 25 m s–1 at an altitude of 210 km above the reference level 5000 = 1 and increases vertically with a scale height of 750 ± 400 km.  相似文献   

20.
An object located approximately atl=8°,b=–4° with a mean radial velocity of –212.3 km s–1 has been observed in the 21 cm neutral hydrogen line. The mean weighted velocity dispersion is 11.2 km s–1 and the total mass is estimated to be 190R 2 (kpc) solar masses. We discuss possible interpretations of the origin and nature of this object. The most likely interpretation is that we observe an expanding object which has been ejected from the galactic nucleus.  相似文献   

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