scholarly journals Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid

2014 ◽  
Vol 26 (28) ◽  
pp. 285101 ◽  
Author(s):  
Buyukdagli Sahin ◽  
Blossey Ralf
Keyword(s):  
Coulomb Fluid

scholarly journals Monte Carlo calibration of avalanches described as Coulomb fluid flows

2005 ◽  
Vol 363 (1832) ◽  
pp. 1529-1550 ◽  
Author(s):  
Christophe Ancey
Keyword(s):  
Friction Coefficient ◽  
Field Data ◽  
Empirical Distribution ◽  
Fluid Flows ◽  
Random Variable ◽  
Data Uncertainty ◽  
Snow Avalanches ◽  
Friction Law ◽  
Field Evidence ◽  
Coulomb Fluid

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

scholarly journals Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble

2019 ◽  
Vol 09 (02) ◽  
pp. 2050016 ◽  
Author(s):  
Chao Min ◽  
Yang Chen
Keyword(s):  
Asymptotic Behavior ◽  
Compatibility Condition ◽  
Logarithmic Derivative ◽  
Hankel Determinant ◽  
Ladder Operators ◽  
Coupled Riccati Equations ◽  
Coulomb Fluid ◽  
Laguerre Unitary Ensemble ◽  
Soft Edge ◽  
Unitary Ensemble

In this paper, we study the Hankel determinant associated with the degenerate Laguerre unitary ensemble (dLUE). This problem originates from the largest or smallest eigenvalue distribution of the dLUE. We derive the ladder operators and its compatibility condition with respect to a general perturbed weight function. By applying the ladder operators to our problem, we obtain two auxiliary quantities [Formula: see text] and [Formula: see text] and show that they satisfy the coupled Riccati equations, from which we find that [Formula: see text] satisfies the Painlevé V equation. Furthermore, we prove that [Formula: see text], a quantity related to the logarithmic derivative of the Hankel determinant, satisfies both the continuous and discrete Jimbo–Miwa–Okamoto [Formula: see text]-form of the Painlevé V. In the end, by using Dyson’s Coulomb fluid approach, we consider the large [Formula: see text] asymptotic behavior of our problem at the soft edge, which gives rise to the Painlevé XXXIV equation.

scholarly journals Electric field fluctuations in the two-dimensional Coulomb fluid

2021 ◽  
Author(s):  
Callum Gray ◽  
Steven T Bramwell ◽  
Peter C W Holdsworth
Keyword(s):  
Electric Field ◽  
Two Dimensional ◽  
Field Fluctuations ◽  
Coulomb Fluid

scholarly journals Statistical Mechanics of Quantum Plasmas Path Integral Formalism

1994 ◽  
Vol 147 ◽  
pp. 43-77
Author(s):  
A. Alastuey
Keyword(s):  
Statistical Mechanics ◽  
Path Integral ◽  
Equations Of State ◽  
Classical System ◽  
Potential Method ◽  
Low Density ◽  
Fixed Temperature ◽  
Path Integral Representation ◽  
Density Expansions ◽  
Coulomb Fluid

AbstractIn this review, we consider a quantum Coulomb fluid made of charged point particles (typically electrons and nuclei). We describe various formalisms which start from the first principles of statistical mechanics. These methods allow systematic calculations of the equilibrium quantities in some particular limits. The effective-potential method is evocated first, as well as its application to the derivation of low-density expansions. We also sketch the basic outlines of the standard many-body perturbation theory. This approach is well suited for calculating expansions at high density (for Fermions) or at high temperature. Eventually, we present the Feynman-Kac path integral representation which leads to the introduction of an auxiliary classical system made of extended objects, i.e., filaments (also called “polymers”). The familiar Abe-Meeron diagrammatic series are then generalized in the framework of this representation. The truncations of the corresponding virial-like expansions provide equations of state which are asymptotically exact in the low-density limit at fixed temperature. The usefulness of such equations for describing the inner regions of the sun is briefly illustrated.

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