scholarly journals PRESSURE LAWS AND FAST LEGENDRE TRANSFORM

2011 ◽  
Vol 21 (04) ◽  
pp. 745-775 ◽  
Author(s):  
P. HELLUY ◽  
H. MATHIS
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Energy Minimization ◽  
Legendre Transform ◽  
Mathematical Tool ◽  
Minimization Principle ◽  
Algebra Theory ◽  
Mixture Thermodynamics ◽  
Two Phases ◽  
Fast Legendre Transform

In this paper we investigate algorithms based on the Fast Legendre Transform (FLT) in order to compute tabulated Equation Of State (EOS) for fluids with phase transition. The equation of state of a binary mixture is given by an energy minimization principle. According to the miscible or immiscible nature of the mixture, the energy of the system is either a convex envelope or an inf-convolution of the energies of the two phases. Because these operations are closely linked to Legendre transform, it is possible to construct fast algorithms that compute efficiently these operations. In addition, it appears that the natural mathematical tool for studying mixture thermodynamics in the Legendre space is the max-plus algebra theory.

scholarly journals NON-UNIFORM STRUCTURE OF MATTER AND THE EQUATION OF STATE

2008 ◽  
Vol 17 (09) ◽  
pp. 1774-1789
Author(s):  
TOSHIKI MARUYAMA ◽  
SATOSHI CHIBA ◽  
TOSHITAKA TATSUMI
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Coulomb Repulsion ◽  
Mixed Phase ◽  
Uniform Structure ◽  
Kaon Condensation ◽  
Maxwell Construction ◽  
Two Phases ◽  
First Order Phase ◽  
Quark Phase

We investigate the non-uniform structures and the equation of state (EOS) of nuclear matter in the context of the first-order phase transitions (FOPT) such as liquid-gas phase transition, kaon condensation, and hadron-quark phase transition. During FOPT the mixed phases appear, where matter exhibits non-uniform structures called "Pasta" structures due to the balance of the Coulomb repulsion and the surface tension between two phases. We treat these effects self-consistently, properly taking into account of the Poisson equation and the Gibbs conditions. Consequently, they make the EOS of the mixed phase closer to that of Maxwell construction due to the Debye screening. This is a general feature of the mixed phase consisting of many species of charged particles.

Equation of State and Phase Transition of the Spherical Lattice Gas

1960 ◽  
Vol 120 (1) ◽  
pp. 22-32 ◽  
Author(s):  
Walter Pressman ◽  
Joseph B. Keller
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Lattice Gas

Equation of state and phase transition of antigorite under high pressure and high temperature

2014 ◽  
Vol 228 ◽  
pp. 56-62 ◽  
Author(s):  
Cuiping Yang ◽  
Toru Inoue ◽  
Akihiro Yamada ◽  
Takumi Kikegawa ◽  
Jun-ichi Ando
Keyword(s):  
Phase Transition ◽  
High Pressure ◽  
High Temperature ◽  
Equation Of State

scholarly journals Constraints on the hybrid equation of state with a crossover hadron-quark phase transition in the light of GW170817

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Cheng-Ming Li ◽  
Yan Yan ◽  
Jin-Jun Geng ◽  
Yong-Feng Huang ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Quark Phase

Solvatomorphs of (Bu4N)2[{Ag(N2-py)}2Mo8O26]: structure, colouration and phase transition

CrystEngComm ◽  
2021 ◽  
Author(s):  
Pavel A Abramov ◽  
Vladislav Komarov ◽  
Denis P Pishchur ◽  
Veronica S. Sulyaeva ◽  
Enrico Benassi ◽  
...  
Keyword(s):  
Phase Transition ◽  
Self Assembly ◽  
Two Phases

Self-assembly of (Bu4N)4[β-Mo8O26], AgNO3 and N2-py (N2-py = 2,6-diaminopyridine) in DMF solution results in (Bu4N)2[β-{Ag(N2-py)}2Mo8O26] complex which crystallises as two phases: one (OP) is orange in colour and consists of...

Topotactic, pressure-driven, diffusion-less phase transition of layered CsCoO2 to a stuffed cristobalite-type configuration

2019 ◽  
Vol 75 (4) ◽  
pp. 704-710
Author(s):  
Naveed Zafar Ali ◽  
Branton J. Campbell ◽  
Martin Jansen
Keyword(s):  
Phase Transition ◽  
High Pressure ◽  
Three Dimensional ◽  
Phase Cell ◽  
Ambient Conditions ◽  
Space Group ◽  
Layered Architecture ◽  
Β Phase ◽  
Vertex Sharing ◽  
Two Phases

CsCoO2, featuring a two-dimensional layered architecture of edge- and vertex-linked CoO4 tetrahedra, is subjected to a temperature-driven reversible second-order phase transformation (α → β) at 100 K, which corresponds to a structural relaxation with concurrent tilting and breathing modes of edge-sharing CoO4 tetrahedra. In the present investigation, it was found that pressure induces a phase transition, which encompasses a dramatic change in the connectivity of the tetrahedra. At 923 K and 2 GPa, β-CsCoO2 undergoes a first-order phase transition to a new quenchable high-pressure polymorph, γ-CsCoO2. It is built up of a three-dimensional cristobalite-type network of vertex-sharing CoO4 tetrahedra. According to a Rietveld refinement of high-resolution powder diffraction data, the new high-pressure polymorph γ-CsCoO2 crystallizes in the tetragonal space group I41/amd:2 (Z = 4) with the lattice constants a = 5.8711 (1) and c = 8.3214 (2) Å, corresponding to a shrinkage in volume by 5.7% compared with the ambient-temperature and atmospheric pressure β-CsCoO2 polymorph. The pressure-induced transition (β → γ) is reversible; γ-CsCoO2 stays metastable under ambient conditions, but transforms back to the β-CsCoO2 structure upon heating to 573 K. The transformation pathway revealed is remarkable in that it is topotactic, as is demonstrated through a clean displacive transformation track between the two phases that employs the symmetry of their common subgroup Pb21 a (alternative setting of space group No. 29 that matches the conventional β-phase cell).

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