Stability of Accretion Discs around Magnetized Stars

We study the stability of accretion disc around magnetised stars. Starting from the equations of magnetohydrodynamics we derive equations for linearized perturbation of geometrically thin, optically thick axisymmetric accretion disc with an internal dynamo around magnetized stars. The structure and evolution of such discs are governed by an evolution equation for matter surface density ∑(R,T). Using the time-dependent equations for an accretion disc we do a linear stability analysis of our steady disc solutions in the presence of the magnetic field generated due to an internal dynamo.

Analysis of Dynamics of Boundary Shape Perturbation of a Rotating Elastoplastic Radially Inhomogeneous Plane Circular Disk: Analytical Approach

For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plastic zone critical radius is obtained as a first approximation. A formula of critical angular velocity is derived which determines the stability loss of the disc according to the self-balanced form. Efficiency of the proposed method is shown by an illustrative example considered in Section 7. Values of critical angular velocity of rotation are found numerically for different parameters of the disc.

Stability Loss of Rotating Elastoplastic Discs of the Specific Form

A method of calculating a possible stability loss by a rotating circular annular disc of variable thickness is suggested within the theory of perfect plasticity with the help of small parameter method. A characteristic equation for a critical radius of a plastic zone is obtained as a first approximation. The formula for the critical angular velocity, determining the stability loss of the disc according to the self-balanced form, is derived. The method using which we can take into account the disc’s geometry and loading parameters is also specified. The efficiency of the proposed method is shown in Section 5 while considering an illustrative example. The values of critical angular velocity of rotating are found numerically for different parameters of the disc.

有限厚度吸积盘对标准薄盘静态结构和稳定性的影响

对标准薄盘模型,当吸积率M大于某临界值M_B时吸积盘的静态平衡结构将是不稳定的,同时原来的薄盘近似h≡H/R(?)1也不再成立。采用微扰论的方法研究了当h(?)1不成立但仍有h<1时的有限厚度对吸积盘静态结构及其稳定性的影响。结果表明,它使平衡曲线除原有的稳定分支和不稳定分支外,将增加1条新的稳定分支,即M(∑)平衡曲线具有“S”形特征,因而存在极限环演化行为。

求解一类非线性算子方程组的扰动迭代序列的稳定性

利用Huang和Fang提出的广义m-增生映象的预解算子技巧,文章构造了一种新的扰动迭代算法2.1,并讨论了迭代算法2.1产生的序列{(x_n,y_n)},关于Banach空间中一类关联于广义m-增生映象的广义预解算子方程组(1.1)的解的收敛性和稳定性。主要结果定理2.1改善并推广了文献[1-3]的相应结果。

α盘的β分布和稳定性

本文在消光系数κ=κ_0ρ~aT^b的假设下讨论了a粘滞律吸积盘的静态平衡结构,尤其是其压力参数β的分布特征。并由Piran判据出发得到了吸积盘的稳定性条件与消化幂指数(a,b)之间的关系。