scholarly journals Three-body hypernetted-chain equation and its numerical solution

2002 ◽  
Vol 117 (1) ◽  
pp. 277-281 ◽  
Author(s):  
Kang Kim ◽  
Toyonori Munakata
Keyword(s):  
Numerical Solution ◽  
Chain Equation ◽  
Hypernetted Chain ◽  
Three Body

scholarly journals The Binding-Energy Distribution of the Binaries in a Star Cluster

1980 ◽  
Vol 85 ◽  
pp. 363-364
Author(s):  
John M. Retterer
Keyword(s):  
Kinetic Equation ◽  
Binding Energy ◽  
Energy Distribution ◽  
Numerical Solution ◽  
Star Cluster ◽  
Initial State ◽  
Encounter Rates ◽  
Self Similar Solution ◽  
Self Similar ◽  
Three Body

In order to study the development of the binding-energy distribution of hard binaries in a star cluster, solutions of the appropriate kinetic equation have been obtained, using the three-body encounter rates calculated by Heggie (1975). The binaries in a homogeneous, time-independent stellar medium are considered first. We calculate an analytical solution, of self-similar form, that can be applied to very hard binaries. Integrated forward in time from an initial state containing no hard binaries, a numerical solution of the kinetic equation rapidly approaches the equilibrium ‘Saha’ form of the energy distribution at small energies, while at high energies the numerical solution behaves like our analytical self-similar solution. The fluctuations in the distribution, due to the stochastic nature of binary creation and evolution, are analyzed. We calculate the rate of exchange encounters when stars of different masses are present; these rates are then combined with the other Heggie rates to find the binary distribution in a multi-mass environment. Next, the creation rate as a function of energy is obtained for the binaries that form in two-body, tidally dissipative encounters. This rate is combined with the three-body encounter rates to calculate how the energy distribution of the tidal binaries evolves. Finally, the binding-energy distribution of hard binaries is obtained in a more realistic inhomogeneous, time-dependent cluster model. Although the evolution of the cluster is governed primarily by the effects of two-body relaxation, the influence of the binaries on the cluster is considered as well. A detailed report of this study has been submitted to The Astronomical Journal.

scholarly journals VARIATIONAL ANALYSIS OF FLAT-TOP SOLITONS IN BOSE–EINSTEIN CONDENSATES

2011 ◽  
Vol 25 (18) ◽  
pp. 2427-2440 ◽  
Author(s):  
B. B. BAIZAKOV ◽  
A. BOUKETIR ◽  
A. MESSIKH ◽  
A. BENSEGHIR ◽  
B. A. PUMAROV
Keyword(s):  
Numerical Solution ◽  
Trial Function ◽  
Variational Analysis ◽  
Dynamic Properties ◽  
Matter Wave ◽  
Variational Approximation ◽  
Pitaevskii Equation ◽  
Three Body ◽  
Bose Einstein ◽  
Good Agreement

Static and dynamic properties of matter-wave solitons in dense Bose–Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross–Pitaevskii equation shows good agreement, thereby validating the proposed approach.

scholarly journals A fast method of solving the hypernetted-chain equation for molecular Lennard-Jones fluids

1995 ◽  
Vol 84 (4) ◽  
pp. 743-755 ◽  
Author(s):  
J.A. Anta ◽  
E. Lomba ◽  
C. Martín ◽  
M. Lombardero ◽  
F. Lado
Keyword(s):  
Fast Method ◽  
Lennard Jones ◽  
Chain Equation ◽  
Hypernetted Chain

Analysis of the hypernetted chain equation for ionic fluids

1993 ◽  
Vol 79 (3) ◽  
pp. 523-536 ◽  
Author(s):  
Johan S. Høye ◽  
Enrique Lomba ◽  
George Stell
Keyword(s):  
Ionic Fluids ◽  
Chain Equation ◽  
Hypernetted Chain
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