Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble

1997 ◽  
Vol 49 (1) ◽  
pp. 124-134
Author(s):  
D. Ya. Petrina ◽  
E. D. Petrina
Keyword(s):  
Canonical Ensemble ◽  
Hard Spheres ◽  
Grand Canonical Ensemble ◽  
Equilibrium States ◽  
Existence Of Equilibrium ◽  
Frame Work ◽  
Grand Canonical

scholarly journals Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures

2020 ◽  
Vol 65 (11) ◽  
pp. 963
Author(s):  
К.А. Bugaev ◽  
O.I. Ivanytskyi ◽  
B.E. Grinyuk ◽  
I.P. Yakimenko
Keyword(s):  
Phase Transition ◽  
Equations Of State ◽  
Canonical Ensemble ◽  
Hard Spheres ◽  
Hard Core ◽  
Grand Canonical Ensemble ◽  
Einstein Condensation ◽  
Dirac Particles ◽  
Bose Einstein ◽  
Grand Canonical

We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.

scholarly journals Phase diagram of brittle fracture in the semi-grand-canonical ensemble

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
T. Mulla ◽  
S. Moeini ◽  
K. Ioannidou ◽  
R. J.-M. Pellenq ◽  
F.-J. Ulm
Keyword(s):  
Phase Diagram ◽  
Brittle Fracture ◽  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Grand Canonical
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