摘要:

It is shown that, in a galactic disk of finite thickness, the growth rate of a spiral mode is considerably reduced compared with that in the zero-thickness disk. Thus, the effect of finite thickness tends to limit the growth rate so that it will not be so high as to prevent the spiral mode from reaching a stationary state. On the other hand, for reasonable galactic models, the reduced growth rate is still high enough to overcome the dissipation due to turbulence and the shock wave in the interstellar medium, so that a quasi-stationary spiral structure can be maintained.

ISSN:0309-1929    

DOI:10.1080/03091928208208998

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A three-dimensional asymptotic density-potential relation is established for a spiral galaxy with a disk of finite thickness. This relation is accurate to the order /kr/−3, where k is the radial wave number and r is the radial distance from the center of the galaxy. In the case of small disk thickness, some simpler and more explicit relations are obtained with the accuracy of order /kr/−2, which is usually sufficient for the discussion of spiral mode. A density-potential relation, accurate to the order /kr/−3, is also obtained for the zero-thickness disk. To the order /kr/−2, this relation reduces to that given earlier by Bertin and Mark (1979), but the present derivation is simpler. The dynamical effect of the density-potential relation for a disk of finite thickness is investigated in Yue (1981).

ISSN:0309-1929    

DOI:10.1080/03091928208208999

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The asymptotic solution and the quantum condition of an eigen-value problem which appears in the density wave theory of the spiral galaxy are re-examined from a mathematical point of view. The dependence of the complex eigen-frequency ω on a large parameter λ is carefully discussed. It turns out that, in the expansion ω=∑χi=oωj/λj, the first term ωo must be real in order that the radiation condition may be satisfied. A related conclusion is that the quantum condition may be expressed in terms of an integral along the real axis of the complex plane of the independent variable. This form for the complex quantum condition is convenient not only for determining the complex eigen-frequency numerically, but also for drawing some physically interesting conclusions directly.

ISSN:0309-1929    

DOI:10.1080/03091928208209000

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Evolution of initially smooth perturbations in a cold self-gravitating medium in a Friedmann Universe gives rise to the formation of singularities in the distribution of density in a manner similar to that of catastrophe theory. Using the approximate nonlinear theory of gravitational instability the objects formed were found to possess a very oblate shape–a “pancake” (Zeldovich, 1970). This result is shown in this paper to be a general feature of the evolution of so-called Lagrangian systems (Arnold, 1980). Pancakes are one of the several kinds of generic singularity formed at the nonlinear stage of evolution of such a system. Some of the others are a cusp, a beak-to-beak, a swailow-tail. In this paper we present the full list of singularities for the one- and two-dimensional cases (Figures 1-9). The three dimensional singularities will be discussed in Part II of the paper. We discuss the geometrical and some dynamical properties of each kind of singularity. We give also asymptotic laws for the growth of the density near each kind of singularity. This list of singularities gives the elements from which the large scale structure of the Universe is constructed.

ISSN:0309-1929    

DOI:10.1080/03091928208209001

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A derivation of two-point Markovian closure is presented in classical statistical field theory formalism. It is emphasized that the procedures used in this derivation are equivalent to those employed in the quantum statistical field theory derivation of the Boltzmann equation. Application of these techniques to the study of two-dimensional flow on a β-plane yields a quasi-homogeneous, quasi-stationary transport equation and a renormalized dispersion relation for Rossby waves

ISSN:0309-1929    

DOI:10.1080/03091928208209002

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor