Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle

Nature ◽  
1993 ◽  
Vol 361 (6414) ◽  
pp. 699-704 ◽  
Author(s):  
Paul J. Tackley ◽  
David J. Stevenson ◽  
Gary A. Glatzmaier ◽  
Gerald Schubert
Keyword(s):  
Phase Transition ◽  
Spherical Model ◽  
Earth’S Mantle

scholarly journals Effects of multiple phase transitions in a three-dimensional spherical model of convection in Earth's mantle

1994 ◽  
Vol 99 (B8) ◽  
pp. 15877 ◽  
Author(s):  
Paul J. Tackley ◽  
David J. Stevenson ◽  
Gary A. Glatzmaier ◽  
Gerald Schubert
Keyword(s):  
Phase Transitions ◽  
Three Dimensional ◽  
Spherical Model ◽  
Earth’S Mantle ◽  
Multiple Phase

Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Chjan C. Lim
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Critical Temperature ◽  
Partition Function ◽  
Open System ◽  
Ground State ◽  
Spherical Model ◽  
Toroidal Plasmas ◽  
Fixed Energy ◽  
System A

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Chaotic, subduction-like downflows in a spherical model of convection in the Earth's mantle

Nature ◽  
1990 ◽  
Vol 347 (6290) ◽  
pp. 274-277 ◽  
Author(s):  
Gary A. Glatzmaier ◽  
Gerald Schubert ◽  
Dave Bercovici
Keyword(s):  
Spherical Model ◽  
Earth’S Mantle

Finite-size scaling of O(n) models with singular behaviour: Magnetization and susceptibility in the presence of an external field

1991 ◽  
Vol 69 (6) ◽  
pp. 753-760 ◽  
Author(s):  
Scott Allen ◽  
R. K. Pathria
Keyword(s):  
Phase Transition ◽  
External Field ◽  
Order Phase Transition ◽  
Finite Size ◽  
Spherical Model ◽  
Complete Agreement ◽  
Continuous Variables ◽  
First Order Phase Transition ◽  
Transition Formula ◽  
First Order Phase

The analysis of a previous study (Allen and Pathria. Can. J. Phys. 67, 952 (1989)) on finite-size effects in systems with O(n) symmetry [Formula: see text], confined to geometry Ld−d′ × ∞d′ (where d and d′ are continuous variables such that 2 < d′ < d < 4) and subjected to periodic boundary conditions, is extended (i) to include the region of first-order phase transition (T < Tc) as well as the region of second-order phase transition [Formula: see text] and (ii) to allow the presence of an external field H > 0. Predictions, involving both amplitudes and exponents, are made on the magnetization m and susceptibility χ in different regimes of the variables T, H, and L. Analytical verification of the predicted results is carried out in the case of the spherical model of ferromagnetism (n = ∞), and complete agreement is found.

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