A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Meccanica ◽  
2008 ◽  
Vol 44 (3) ◽  
pp. 239-254 ◽  
Author(s):  
J. P. Vishwakarma ◽  
G. Nath
Keyword(s):  
Ideal Gas ◽  
Solid Particles ◽  
Similar Solution ◽  
Shock Propagation ◽  
Self Similar Solution ◽  
Self Similar

Shock propagation in accretion discs around merging black holes: self-similar solution

2020 ◽  
Vol 494 (4) ◽  
pp. 5520-5533
Author(s):  
D V Bisikalo ◽  
A G Zhilkin
Keyword(s):  
Shock Wave ◽  
Black Holes ◽  
Gravitational Wave ◽  
Accretion Disc ◽  
Similar Solution ◽  
Electromagnetic Response ◽  
Shock Propagation ◽  
Binary Black Holes ◽  
Self Similar Solution ◽  
Self Similar

ABSTRACT To date, the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo gravitational wave detectors have registered several events due to merging binary black holes. It is considered that black holes are surrounded by the circumbinary accretion disc therefore such events must be followed by perturbation of the disc and an increase in the flux of electromagnetic radiation from these objects. Our recent numerical investigations have shown that the heating of matter caused by a shock wave leads to an increase in luminosity. This shock wave arises in the accretion disc due to the central object mass loss as a result of the radiation of gravitational waves. In this paper, a self-similar solution is considered. In this solution the accretion disc perturbation is described in a region, dominated by gas pressure, and the matter opacity is determined by Thomson electron scattering processes. Such an analytical model allows us to approximately estimate the magnitude of the electromagnetic response of the gravitational wave event without time-consuming numerical calculations.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

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