Reply to comment on “green's functions in the theories of radiationless transitions, complex molecular spectra and resonant Raman cross sections

Capitalizing on some earlier work, this paper presents a novel Monte Carlo-based approach that allows estimating the neutron noise induced by stationary perturbations of macroscopic cross-sections in the frequency domain. This method relies on the prior computation using Monte Carlo of modified Green’s functions associated to the real part of the dynamic macroscopic cross-sections, mimicking equivalent subcritical problems driven by external neutron sources. Once such modified Green’s functions are estimated, the neutron noise induced by any type of perturbations can be recovered, by solving a linear algebra problem accounting for the interdependence between the real and imaginary parts of the governing balance equations. The newly derived method was demonstrated on a large homogeneous test system and on a small heterogeneous test system to provide results comparable to a diffusion-based solver specifically developed for neutron noise applications. The new method requires the specification by the user of the real part of the Fourier transform of the macroscopic cross-sections. This is accomplished using ACE-formatted cross-section files defined by the user. Beyond this input data preparation, no change to the Monte Carlo source code is necessary. This represents the main advantage of the proposed method as compared to similar efforts requiring extensive modifications to the Monte Carlo source code.

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Permeability Estimation Based on the Geometry of Pore Space via Random Walk on Grids

Geofluids ◽

10.1155/2019/9240203 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Tongchao Nan ◽

Jichun Wu ◽

Kaixuan Li ◽

Jianguo Jiang

Keyword(s):

Random Walk ◽

Cross Sections ◽

Green's Functions ◽

Green’S Functions ◽

Pore Space ◽

Dynamics Simulation ◽

Pore Scale ◽

Permeability Estimation ◽

The Mean

In the literature, the mean penetration depth (MPD) calculated by “walk on spheres” or “walk on cubes” was used to quickly estimate the intrinsic permeability of digitized porous media. However, these two methods encounter difficulties such as irregular boundaries and the determination of arrivals at a boundary. In this study, an MPD method that is based on a more flexible “random walk on grid” (WOG) is explored. Moreover, the accurate MPDs for the pores of simple shapes are derived with Green’s functions to validate the WOG-based MPD. The results suggested that MPDs based on Green’s functions and WOG are consistent with each other; the factor C in the permeability expression is slightly dependent on roundness of the cross sections and is approximately 1.125 on average, according to analytical and numerical results. In a synthetic complex pore, the permeability estimated by WOG is comparable to, but greater than, the estimate based on the pore-scale dynamics simulation in COMSOL.

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