Appendix 6: About self-consistent description of elementary reaction rates and the equilibrium state of reaction systems

2017 ◽  
pp. 629-633
Keyword(s):  
Equilibrium State ◽  
Reaction Rates ◽  
Elementary Reaction ◽  
Reaction Systems ◽  
Consistent Description ◽  
Self Consistent

scholarly journals Coarse-graining via EDP-convergence for linear fast-slow reaction systems

2020 ◽  
Vol 30 (09) ◽  
pp. 1765-1807 ◽  
Author(s):  
Alexander Mielke ◽  
Artur Stephan
Keyword(s):  
Detailed Balance ◽  
Reaction System ◽  
Gradient Flow ◽  
Coarse Graining ◽  
Reaction Rates ◽  
Coarse Grained ◽  
Gradient Structure ◽  
Reaction Systems ◽  
Fast Reactions ◽  
Finite State

We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarse-grained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system can be written as a gradient flow with respect to the relative entropy. Focusing on the physically relevant cosh-type gradient structure we show how an effective limit gradient structure can be rigorously derived and that the coarse-grained equation again has a cosh-type gradient structure. We obtain the strongest version of convergence in the sense of the Energy-Dissipation Principle (EDP), namely EDP-convergence with tilting.

scholarly journals Self-consistent description of finite nuclei based on a relativistic quark model

1996 ◽  
Vol 609 (3) ◽  
pp. 339-363 ◽  
Author(s):  
Koichi Saito ◽  
Kazuo Tsushima ◽  
Anthony W. Thomas
Keyword(s):  
Quark Model ◽  
Relativistic Quark Model ◽  
Consistent Description ◽  
Self Consistent ◽  
Finite Nuclei

scholarly journals Self-consistent description of the SHFB equations for 112Sn

2018 ◽  
Vol 8 ◽  
pp. 734-743
Author(s):  
M. Ghafouri ◽  
H. Sadeghi ◽  
M. Torkiha
Keyword(s):  
Consistent Description ◽  
Self Consistent
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