A multi-term trial function stability analysis of isotropic relativistic star clusters

1978 ◽  
Vol 55 (2) ◽  
pp. 351-382
Author(s):  
Kevin G. Suffern
Keyword(s):  
Stability Analysis ◽  
Trial Function ◽  
Star Clusters ◽  
Relativistic Star ◽  
Term Trial

Relativistic star clusters with high central redshift

Pramana ◽  
1980 ◽  
Vol 15 (1) ◽  
pp. 53-63
Author(s):  
M C Durgapal ◽  
P S Rawat ◽  
R Banerji
Keyword(s):  
Star Clusters ◽  
Relativistic Star

The dynamic instability of isothermal relativistic star clusters

1976 ◽  
Vol 203 ◽  
pp. 477 ◽  
Author(s):  
K. G. Suffern ◽  
E. D. Fackerell
Keyword(s):  
Dynamic Instability ◽  
Star Clusters ◽  
Relativistic Star

Water wave scattering by a step of arbitrary profile

2000 ◽  
Vol 411 ◽  
pp. 131-164 ◽  
Author(s):  
R. PORTER ◽  
D. PORTER
Keyword(s):  
Water Waves ◽  
Trial Function ◽  
Fluid Velocity ◽  
Equation System ◽  
Constant Depth ◽  
Incoming Wave ◽  
Water Wave Scattering ◽  
Term Trial ◽  
Judicious Choice ◽  
Fluid Behaviour

The two-dimensional scattering of water waves over a finite region of arbitrarily varying topography linking two semi-infinite regions of constant depth is considered. Unlike many approaches to this problem, the formulation employed is exact in the context of linear theory, utilizing simple combinations of Green's functions appropriate to water of constant depth and the Cauchy–Riemann equations to derive a system of coupled integral equations for components of the fluid velocity at certain locations. Two cases arise, depending on whether the deepest point of the topography does or does not lie below the lower of the semi-infinite horizontal bed sections. In each, the reflected and transmitted wave amplitudes are related to the incoming wave amplitudes by a scattering matrix which is defined in terms of inner products involving the solution of the corresponding integral equation system.This solution is approximated by using the variational method in conjunction with a judicious choice of trial function which correctly models the fluid behaviour at the free surface and near the joins of the varying topography with the constant-depth sections, which may not be smooth. The numerical results are remarkably accurate, with just a two-term trial function giving three decimal places of accuracy in the reflection and transmission coefficents in most cases, whilst increasing the number of terms in the trial function results in rapid convergence. The method is applied to a range of examples.

Relativistic Stellar Dynamics in Rotating Axially Symmetric Systems

1968 ◽  
Vol 1 (3) ◽  
pp. 86-87 ◽  
Author(s):  
E.D. Fackerell
Keyword(s):  
General Relativity ◽  
Star Clusters ◽  
Stellar Dynamics ◽  
Spherically Symmetric ◽  
Axially Symmetric ◽  
Relativistic Star ◽  
General Relativistic ◽  
Stellar Sources ◽  
Symmetric Systems

Recently the possibility has been raised of using general relativistic star clusters as models for quasi-stellar sources. The theory of static, spherically symmetric, collisionless star clusters has been developed within the framework of general relativity. In particular, analogues have been found of the Newtonian polytropic models and of Woolley’s truncated Maxwellian systems. However, in view of the importance of rotation on stability in relativistic astrophysical problems, it is of considerable interest to include the effect of rotation in relativistic stellar dynamics.

scholarly journals The Structure and Dynamic Instability of Isothermal Relativistic Star Clusters

1976 ◽  
Vol 29 (4) ◽  
pp. 311 ◽  
Author(s):  
Edward D Fackerell ◽  
Kevin G Suffern
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Rest Mass ◽  
Star Clusters ◽  
Relativistic Star ◽  
The Stability

The structure and dynamic stability of isothermal relativistic star clusters are discussed both for the case of clusters without dispersion in stellar rest mass and for two families of clusters with dispersion in stellar rest mass. We show that the former are dynamically unstable if the central redshift is greater than about 0'5, and that the latter are dynamically unstable if the central redshift is greater than about O' 6, so that the inclusion of dispersion in mass does not greatly affect the stability of isothermal relativistic star clusters.

scholarly journals The Concentric Shell Method for Relativistic Star Clusters

1975 ◽  
Vol 69 ◽  
pp. 433-439 ◽  
Author(s):  
E. D. Fackerell
Keyword(s):  
Star Clusters ◽  
Spherically Symmetric ◽  
Spherical Shells ◽  
Relativistic Star ◽  
Symmetric Star ◽  
Concentric Shell

The analytic aspects of the Campbell-Hénon method of concentric spherical shells are generalized for application to relativistic spherically symmetric star clusters.

On the existence of stable relativistic star clusters with arbitrarily large central redshifts

1989 ◽  
Vol 336 ◽  
pp. L63 ◽  
Author(s):  
Frederic A. Rasio ◽  
Stuart L. Shapiro ◽  
Saul A. Teukolsky
Keyword(s):  
Star Clusters ◽  
Relativistic Star
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