Monte Carlo studies on the long time dynamic properties of dense cubic lattice multichain systems. I. The homopolymeric melt

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

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Monte Carlo studies of percolation phenomena for a simple cubic lattice

Journal of Statistical Physics ◽

10.1007/bf01020338 ◽

1976 ◽

Vol 15 (5) ◽

pp. 345-353 ◽

Cited By ~ 85

Author(s):

Amit Sur ◽

Joel L. Lebowitz ◽

J. Marro ◽

M. H. Kalos ◽

S. Kirkpatrick

Keyword(s):

Monte Carlo ◽

Cubic Lattice ◽

Simple Cubic ◽

Simple Cubic Lattice ◽

Monte Carlo Studies ◽

Percolation Phenomena

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Monte Carlo studies of percolation phenomena for a simple cubic lattice

Journal of Aerosol Science ◽

10.1016/0021-8502(76)90061-6 ◽

1976 ◽

Vol 7 (6) ◽

pp. 509

Keyword(s):

Monte Carlo ◽

Cubic Lattice ◽

Simple Cubic ◽

Simple Cubic Lattice ◽

Monte Carlo Studies ◽

Percolation Phenomena

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Monte Carlo studies of the cubic lattice mixed-bond Ising model

Physica B Condensed Matter ◽

10.1016/j.physb.2007.04.031 ◽

2007 ◽

Vol 398 (2) ◽

pp. 294-296 ◽

Cited By ~ 8

Author(s):

J.B. Santos-Filho ◽

N.O. Moreno ◽

D.F. de Albuquerque ◽

A.S. de Arruda

Keyword(s):

Monte Carlo ◽

Ising Model ◽

Cubic Lattice ◽

Monte Carlo Studies

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Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

Nuclear Fusion ◽

10.1088/1741-4326/ac4777 ◽

2021 ◽

Author(s):

Frederick Law ◽

Antoine J Cerfon ◽

Benjamin Peherstorfer

Keyword(s):

Monte Carlo ◽

Surrogate Model ◽

Energetic Particle ◽

Small Time ◽

Point Of View ◽

High Fidelity ◽

Monte Carlo Studies ◽

Long Time ◽

Particle Confinement ◽

Fidelity Model

Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

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