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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.
An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10–36 (k=+1), +3×10–35 (k=0), +10–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.  相似文献   

3.
The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than B x 2 /B 0 2 . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients 2/t=2D and /t=D /, and that all higher-order coefficients are identically zero.  相似文献   

4.
A maximal spectrum of gravitational radiation from sources outside our galaxy is calculated. The sources are galaxies, quasars and events that occur in the early history of the universe. The major contribution is from galaxies whose effect extends over the frequency region 10–810+4Hz, peaking at 10–110 Hz, with a spectral flux of 10 erg cm–2, s–1. The main processes of gravitational radiation in the galaxies are stellar collapse into a black hole and dying binary systems. In the region 10–4104 Hz the background spectrum is well above the detection levels of currently proposed detectors. FromMinimal considerations of this spectrum it is determined that the density of gravitational radiation is 10–39g cm–3. This background spectrum is sensitive to galactic evolution and especially sensitive to the upper mass limits and mass distribution of stars in galactic models. Therefore, the spectrum could provide information about galactic evolution complementary to that obtained by electromagnetic investigations.  相似文献   

5.
An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg*(C –C )/U 0 3 ) - Pr Prandtl number (C p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U 0) - v normal velocity component - v 0 suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C p specific heat at constant pressure - C w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C w -C )) - Gr Grashof number (g(T w -T )/U 0 3 ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU 0 2 /) - U 0 reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U 0) - v dimensionless velocity (v/U 0) - v 0 non-dimensionalv 0 (v 0 /U0)=–at–1/2 - y dimensionless ordinate (yU 0/) - density of the fluid - coefficient of viscosity  相似文献   

6.
We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (103109 eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() –5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), M 8×106, corresponds to the upper cut-off energy of the -ray spectrum, 109 eV. The lower limit to the momentum, m 1.8×105, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.  相似文献   

7.
A fifth list of point sources from the IRAS Point Source Catalog (PSC) that are optically identified with stars of late spectral types is given. The list contains data on 75 objects. The identifications were based on the Digital Sky Survey (DSS), the First Byurakan Survey, blue and red maps of the Palomar Observatory Sky Survey, and infrared fluxes at the wavelengths 12, 25, 60, and 100 m in the regions of +73° +80° and 03h30m 18h30m and of +80° +90° and 00h00m 20h00m. Of the 99 objects, which are given in the IRAS PSC as unidentified sources of infrared emission, 24 are associated with known stars in existing catalogs while 75 sources proved to be unknown in the optical range. The optical coordinates, their departures from the IR coordinates, the V stellar magnitudes, the color indices CI, and the preliminary spectral subtypes have been determined. The objects have optical magnitudes in the range of 6 m .5-17 m .2. Finder charts from the DSS are given for the 69 new objects.  相似文献   

8.
A study is made of Lyman continuum observations of solar flares, using data obtained by the Harvard College Observatory EUV spectroheliometer on the Apollo Telescope Mount. We find that there are two main types of flare regions: an overall mean flare coincident with the H flare region, and transient Lyman continuum kernels which can be identified with the H and X-ray kernels observed by other authors. It is found that the ground level hydrogen population in flares is closer to LTE than in the quiet Sun and active regions, and that the level of Lyman continuum formation is lowered in the atmosphere from a mass column density m 5/sx 10–6 g cm–2 in the quiet Sun to m 3/sx 10–4 g cm–2 in the mean flare, and to m 10–3g cm–2 in kernels. From these results we derive the amount of chromospheric material evaporated into the high temperature region, which is found to be - 1015g, in agreement with observations of X-ray emission measures. A comparison is made between kernel observations and the theoretical predictions made by model heating calculations, available in the literature; significant discrepancies are found between observation and current particle-heating models.  相似文献   

9.
A list of objects of the BIG (Byurakan-IRAS galaxies) sample is given: 89 galaxies identified with 55 point sources from the IRAS Point Source Catalog. The identifications were based on the Digital Sky Survey (DSS), the First Byurakan Survey, blue and red maps of the Palomar Observatory Sky Survey, and infrared fluxes at wavelengths of 12, 25, 60, and 100 mm in the region of +61° +65° and 05h30m 18h 00m with an area of 340 deg2 (additional IR sources were identified). The optical coordinates of the identified galaxies, their departure from the IR coordinates, the V stellar magnitude, morphological type, angular size, and position angle were determined. The objects have optical magnitudes in the range of 12 m .5 - 21 m .5 and angular sizes in the range of 3 - 43. Finder charts for these objects from the DSS are given.  相似文献   

10.
An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension ik . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p / (,p, p are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c2 in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.  相似文献   

11.
Apparent radius, visual brightness, effective temperature and absolute radius for 416 B5 v-F5 v stars of the catalogue of the Geneva Observatory (Rufener, 1976) have been determined.Twenty-eight stars, anomalous in log versus (m v)0 diagrams, have been singled out. A good correlation for seven stars, in common with the list of Hanbury Brownet al. (1974), has been found. Similar parameters determined for 279 B5 v-F5 v stars of two preceding papers (Fracassiniet al., 1973, 1975) have allowed us to determine the averaged diagrams logq v/q, logR/R and logT e versus (B-V)0 for 695 B5 v-F5 v stars.Moreover, in the present paper a good correlation logq v/q versus logR/R and careful relation M v=–7.40logR/R +3.31 for B5 v-F5 v stars have been determined. Plain correlations between logR/R and blanketing parameterm 2 for some spectral types seem to point out that there arereal differences in the absolute radii of stars of thesame spectral type, in agreement with recent researches on the HR diagram (Houck and Fesen, 1978).Systematic differences between double (spectroscopic and visual) and single stars are found. In particular, the averaged relation m 2 versus logR/R shows that A2 v-F5 v double stars may have a higher metallicity indexm 2 and smaller absolute radii than single stars. Finally, the diagram logv sini versus logR/R confirms some properties of binary systems found by other researchers (Huang, 1966; Plavec, 1970; Levato, 1974; Kitamura and Kondo, 1978).Thesis for the degree in Applied Physics.  相似文献   

12.
Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB T =13.57 with maximum diameters 1.57×1.34 (at threshold m =27.7 mag.//) andV T =12.91 with maximum diameters 1.54×1.32 (at threshold m =27.7 mag./). The integrated colour index(B–V) T =0.66 and the effective surface brightness e (B=19.0 mag./) and e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr *<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×107 yr.  相似文献   

13.
Hong Wei Li 《Solar physics》1986,104(1):131-136
The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter p / e are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.  相似文献   

14.
Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX 2+,A 22,A22, andA22, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.  相似文献   

15.
General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities 0, where 0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of –-hyperons at > c , where c 40. The electric resistivities along and acrossB, and , and the Hall resistivity H are calculated and fitted by simple analytical formulae at c and > c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If c , one has = [1 + (B/B 0)2] for the normal neutrons, and for the superfluid neutrons, while H = B/B e for both cases. HereB e 109 T 8 2 G,B 01011 T 8 2 G, andT 8 is temperature in units of 108 K. Accordingly for the normal neutrons atBB 0, the transverse resistivity suffers an enhancement, 1/4 1. When 50 andB varies from 0 toBB p 1013 T 8 2 G, increases by a factor of about 103–104 and H changes sign. WhenBB p , remains constant for the superfluid neutrons, and H B 2 for the normal neutrons, while H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.  相似文献   

16.
The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C jk n (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin2t - i inclination of the orbit - J n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S jk n (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M++m) (gravitational constant times the sum of the masses of Earth and satellite) - n,k coefficients ofR component of disturbing acceleration (funtions off) - n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X 0 n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node  相似文献   

17.
Intensity, polarization, and cooling rate of the two-photon annihilation radiation are studied in detail in the case of one-dimensional power-law distributions of electrons and positrons, assuming that they occupy the ground Landau level in a strong magnetic fieldB1010–1012 G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-lawe ± distributions ± ± –k are shown to generate power-law spectra of the annihilation radiation atEmc 2 andEmc 2, with indices depending on the direction of radiation. The annihilation spectra at =0 show the largest blue-shifts of their maxima and the hardest high-energy tailsI(Emc 2, =0)E –(k–1). The blue-shifts reduce, and the hard tials steepen, with increasing . At >(2mc 2/E)1/2 the slopes of the high-energy tails rapidly transform to that at =2,I(Emc 2, =/2)E –(2k+3). The direction-integrated spectraS(E) also display the power-law tials at low and high energies,S(Emc 2)E –(k+1). The total annihilation rate and energy losses decrease with decreasingk, being higher than for the isotropice ± power-law distributions at the samek. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degreeP is maximum atEmc 2:P max0.6 for =/2. Annihilation features and power-law-like hard tails observed in many gamma-ray burst spectra may be associated with the annihilation radiation of the magnetized power-law distributed plasma near neutron stars. Comparison of the observed and theoretical spectra allows one to estimate the power-law index of thee – e +-distribution and the gravitational redshift factor in the radiating region.  相似文献   

18.
We investigate the dynamics and evolution of coalescing neutron stars. The three-dimensional Newtonian equations of hydrodynamics are integrated by the Piecewise Parabolic Method on an equidistant Cartesian grid. The code is purely Newtonian, but does include the emission of gravitational waves and their back-reaction. The properties of neutron star matter are described by the equation of state of Lattimer and Swesty (1991). Energy loss by all types of neutrinos and changes of the electron fraction due to the emission of electron neutrinos and antineutrinos are taken into account by an elaborate neutrino leakage scheme. We simulate the coalescence of two identical, cool neutron stars with a baryonic mass of 1.6M and a radius of 15 km and with an initial center-to-center distance of 42 km. The initial distributions of density and electron concentration are given from a model of a cold neutron star in hydrostatic equilibrium. We investigate three cases which differ by the initial velocity distribution in the neutron stars. The orbit decays due to gravitational-wave emission and after one revolution the stars are so close that dynamical instability sets in. Within 1 ms the neutron stars merge into a rapidly spinning (P 1 ms), high-density body ( 1014 g/cm3) with a surrounding thick disk of material with densities 1010 – 1012 g/cm3 and orbital velocities of 0.3-0.5 c. The peak emission of gravitational waves has a maximum luminosity of a few times 1055 erg/s and is reached for about 1 ms. The amplitudes of the gravitational waves are close to 3 10–23 at a distance of 1 Gpc and the typical frequency is near the dynamical value of the orbital motion of the merging neutron stars of 2 KHz. In a post-processing step, the rate of neutrino-antineutrino annihilation is calculated from the neutrino luminosities generated during the hydrodynamical simulations. We find the integral annihilation rate to be a few 1050 erg/s during the phase of strongest neutrino emission, which is too small to generate the observed bursts considering the fact that the merged object of about 3M will most likely collapse to a black hole within milliseconds.  相似文献   

19.
We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec2 at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C min the H- 1.5 Å image (C m 0.1 type I, C m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C m- A scatter diagram, in H and H wings, indicates a wide range of variability for C m in correspondence with very narrow range of variability for A.  相似文献   

20.
We present an attempt for an extension of the modified Boltzmann model, which was introduced by Callebautet al. (1982) as an improvement of the polytropic models, to the case of chemically-heterogeneous stars in equilibrium, containing H and He, by proposing a density profile of the formp=C 1 T N exp (–H m(–*)/kT) +C 2 T N exp (–He m(–*)/kT. Analytical properties are derived and numerical as well as analytical arguments are presented for the conclusion that this hypothesis for a density profile imposes an almost constant chemical profile to the model as a whole, thereby making it in this form unsuited for the study of heterogeneous stars. A comparison is made with the former Boltzmann model in the homogeneous limit.  相似文献   

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