Influence of Embedded Inhomogeneities on the Spectral Ratio of the Horizontal Components of a Random Field of Rayleigh Waves

Цуканов, А. А.; Gorbatnikov, A. V.

doi:10.1134/s1063771018010189

Cited by 7 publications

(1 citation statement)

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“…Extending the ideas of the classic RFIM, Tadic and collaborators [64] were able to describe critical Barkhausen avalanches in quasi-2D ferromagnets with an open boundary. The use of MRFs with disordered field components has also allowed to characterize embedded inhomogeneities in the spectral properties of Rayleigh waves with application to the study of the Earth's microseismic field [65]. Geoacustic measurements and its MRF modeling allowed these researchers to estimate the mechanical and structural properties of the Earth's crust and upper mantle.…”

Section: Mrfs In Condensed Matter Physics and Materials Sciencementioning

confidence: 99%

Random Fields in Physics, Biology and Data Science

Hernández‐Lemus

2021

Front. Phys.

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A random field is the representation of the joint probability distribution for a set of random variables. Markov fields, in particular, have a long standing tradition as the theoretical foundation of many applications in statistical physics and probability. For strictly positive probability densities, a Markov random field is also a Gibbs field, i.e., a random field supplemented with a measure that implies the existence of a regular conditional distribution. Markov random fields have been used in statistical physics, dating back as far as the Ehrenfests. However, their measure theoretical foundations were developed much later by Dobruschin, Lanford and Ruelle, as well as by Hammersley and Clifford. Aside from its enormous theoretical relevance, due to its generality and simplicity, Markov random fields have been used in a broad range of applications in equilibrium and non-equilibrium statistical physics, in non-linear dynamics and ergodic theory. Also in computational molecular biology, ecology, structural biology, computer vision, control theory, complex networks and data science, to name but a few. Often these applications have been inspired by the original statistical physics approaches. Here, we will briefly present a modern introduction to the theory of random fields, later we will explore and discuss some of the recent applications of random fields in physics, biology and data science. Our aim is to highlight the relevance of this powerful theoretical aspect of statistical physics and its relation to the broad success of its many interdisciplinary applications.

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Section: Mrfs In Condensed Matter Physics and Materials Sciencementioning

confidence: 99%