scholarly journals Second order cumulants of conserved charge fluctuations revisited: Vanishing chemical potentials

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
D. Bollweg ◽  
J. Goswami ◽  
O. Kaczmarek ◽  
F. Karsch ◽  
Swagato Mukherjee ◽  
...  
1985 ◽  
Vol 68 (5) ◽  
pp. 337-341 ◽  
Author(s):  
Myriam S. Giambiagi ◽  
Mario Giambiagi ◽  
Francisco E. Jorge

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 535-549 ◽  
Author(s):  
Duncan Paterson ◽  
Michael L. Michelsen ◽  
Erling H. Stenby ◽  
Wei Yan

Summary Two algorithms are proposed for isothermal multiphase flash. These are referred to as modified RAND and vol-RAND. The former uses the chemical potentials and molar-phase amounts as the iteration variables, while the latter uses chemical potentials and phase volumes to cosolve a pressure-explicit equation of state (EOS) with the equilibrium equations. Compared with the conventional second-order approach using Gibbs-energy minimization, these methods are more structured, with all components in all phases treated in the same way. Both have been derived to include chemical reactions for any number of phases along with the possible simplifications for only phase equilibria. The simple structured implementation of these methods is demonstrated for modified RAND and vol-RAND. The rate of convergence of the methods presented is shown to be the same as the conventional second-order method for isothermal flash. It is demonstrated that the use of an association term [cubic plus association (CPA)] adds little additional computational cost when using vol-RAND compared with a simple cubic Soave-Redlich-Kwong (SRK) without association. The RAND methods scale better in terms of the O(n3) operations as more phases are introduced, and are computationally less expensive than the conventional Gibbs minimization method for more than three phases.


Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT

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