Comparing methods and Monte Carlo algorithms at phase transition regimes: A general overview

2014 ◽  
pp. 3-20
Author(s):  
Carlos E. Fiore
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
General Overview ◽  
Monte Carlo Algorithms

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

scholarly journals Moment-Preserving and Mesh-Adaptive Reweighting Method for Rare-Event Sampling in Monte-Carlo Algorithms

2021 ◽  
pp. 108041
Author(s):  
C.U. Schuster ◽  
T. Johnson ◽  
G. Papp ◽  
R. Bilato ◽  
S. Sipilä ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Rare Event ◽  
Monte Carlo Algorithms

scholarly journals Liquid–liquid phase transition in hydrogen by coupled electron–ion Monte Carlo simulations

2016 ◽  
Vol 113 (18) ◽  
pp. 4953-4957 ◽  
Author(s):  
Carlo Pierleoni ◽  
Miguel A. Morales ◽  
Giovanni Rillo ◽  
Markus Holzmann ◽  
David M. Ceperley
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Density Functional ◽  
Fluid Phase ◽  
Transition Line ◽  
Energy Applications ◽  
First Order Phase Transition ◽  
Fundamental Research ◽  
Diamond Anvil ◽  
First Order Phase

The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron–ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25–30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.

Parallel Monte Carlo algorithms for information retrieval

2003 ◽  
Vol 62 (3-6) ◽  
pp. 289-295 ◽  
Author(s):  
V.N. Alexandrov ◽  
I.T. Dimov ◽  
A. Karaivanova ◽  
C.J.K. Tan
Keyword(s):  
Monte Carlo ◽  
Information Retrieval ◽  
Monte Carlo Algorithms

AVRAMI–KOLMOGOROV–JOHNSON–MEHL KINETICS FOR NANOPARTICLES

2008 ◽  
Vol 15 (05) ◽  
pp. 605-612 ◽  
Author(s):  
VLADIMIR P. ZHDANOV
Keyword(s):  
Phase Transition ◽  
Activation Energy ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Infinite Medium ◽  
Local State ◽  
Elementary Reaction ◽  
Regular Surface

In the conventional Avrami–Kolmogorov–Johnson–Mehl model, the reaction or phase transition occurring in the 2D or 3D infinite medium is considered to start and proceed around randomly distributed and/or appearing nucleation centers. The radius of the regions transformed is assumed to linearly increase with time. The Monte Carlo simulations presented, illustrate what may happen if the transformation takes place in nanoparticles. The attention is focused on nucleation on the regular surface, edge and corner sites, and on the dependence of the activation energy for elementary reaction events on the local state of the sites.

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