Cauchy’s theorem and generalization

Reuss, Paul

doi:10.1051/epjn/2018010

Cited by 2 publications

(2 citation statements)

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“…The second effect introduces a factor of exactly 1 (thus leading to B = n 2 ) in several cases: for non-refractive particles ( n = 1) the photons propagate in straight lines and the mean distance traveled in the particle <l> is given by the Cauchy formula <l > = 4 V/S ( V and S are the volume and surface area of the particle). The same mean distance is obtained for refractive ( n > 1) particles composed of a scattering material 55 because the Cauchy formula holds for a wide class of random walks 51 , 53 . The reason is the compensating effect of scattering: longer tortuous paths are balanced by short paths that escape quickly from the particle.…”

Section: Resultssupporting

confidence: 54%

“…The underlying reason explaining why and when B = n 2 can be established from a series of fundamental studies in mathematics, ecology, optics and nuclear physics 50 – 53 . The absorption within a weakly-absorbing particle is proportional to the mean path traveled by photons in the particle, and B measures how this distance is increased compared to the propagation in a straight line, in the case of diffuse illumination.…”

Section: Resultsmentioning

confidence: 99%

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Unraveling the optical shape of snow

et al. 2023

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The reflection of sunlight off the snow is a major driver of the Earth’s climate. This reflection is governed by the shape and arrangement of ice crystals at the micrometer scale, called snow microstructure. However, snow optical models overlook the complexity of this microstructure by using simple shapes, and mainly spheres. The use of these various shapes leads to large uncertainties in climate modeling, which could reach 1.2 K in global air temperature. Here, we accurately simulate light propagation in three-dimensional images of natural snow at the micrometer scale, revealing the optical shape of snow. This optical shape is neither spherical nor close to the other idealized shapes commonly used in models. Instead, it more closely approximates a collection of convex particles without symmetry. Besides providing a more realistic representation of snow in the visible and near-infrared spectral region (400 to 1400 nm), this breakthrough can be directly used in climate models, reducing by 3 the uncertainties in global air temperature related to the optical shape of snow.

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Section: Resultssupporting

confidence: 54%

Section: Resultsmentioning

confidence: 99%

Unraveling the optical shape of snow

et al. 2023

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SiC Detector Thickness Optimization for Enhanced Response Variability

Belfiore,

Antoni,

Ben Mosbah

et al. 2024

EPJ Web Conf.

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Neutron spectroscopy is a crucial point in several nuclear applications. Accurately measuring fast neutron energy distributions in high-flux conditions reveals a significant technology gap, hindering the acquisition of precise energy fluence distributions. This project investigates the potential of machine learning to bridge this gap, focusing on neutron energies from 100 keV to 20 MeV and fluence rates from 1010 n/cm2s to 1012 n/cm2s using solid detectors such as Silicon Carbide (SiC) and Chemical Vapor Deposition (CVD) diamonds. This paper details the simulation design phase of our project, emphasizing the exploration of optimal SiC solid detector thickness to introduce crucial variability for machine learning training.

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Cauchy’s theorem and generalization

Cited by 2 publications

References 3 publications

Unraveling the optical shape of snow

Unraveling the optical shape of snow

SiC Detector Thickness Optimization for Enhanced Response Variability

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