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1. Enhanced Backscattering of a partially coherent field from an anisotropic random lossy medium

   https://doi.org/doi:10.3934/dcdsb.2020158  

   Garnier, J.; Solna, K. (April 2021, Discrete and continuous dynamical systems)

   null (Ed.)

   The weak localization or enhanced backscattering phenomenon has received a lot of attention in the literature. The enhanced backscattering cone refers to the situation that the wave backscattered by a random medium exhibits an enhanced intensity in a narrow cone around the incoming wave direction. This phenomenon can be analyzed by a formal path integral approach. Here a mathematical derivation of this result is given based on a system of equations that describes the second-order moments of the reflected wave. This system derives from a multiscale stochastic analysis of the wave field in the situation with high-frequency waves and propagation through a lossy medium with fine scale random microstructure. The theory identifies a duality relation between the spreading of the wave and the enhanced backscattering cone. It shows how the cone, its regularity and width relate to the statistical structure of the random medium. We discuss how this information in particular can be used to estimate the internal structure of the random medium based on observations of the reflected wave. 

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2. Fourth-order moments analysis for partially coherent electromagnetic beams in random media

   https://doi.org/10.1080/17455030.2022.2096272  

   Garnier, Josselin; Sølna, Knut (November 2023, Waves in Random and Complex Media)

   A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian–Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources. 

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3. A graphon approach to limiting spectral distributions of Wigner‐type matrices

   https://doi.org/10.1002/rsa.20894  

   Zhu, Yizhe (October 2019, Random Structures & Algorithms)

   We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner‐type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes transforms explicitly with weaker assumptions on the convergence of variance profiles than previous results. As applications, we give a new proof of the semicircle law for generalized Wigner matrices and determine the limiting spectral distributions for three sparse inhomogeneous random graph models with sparsityω(1/n): inhomogeneous random graphs with roughly equal expected degrees,W‐random graphs and stochastic block models with a growing number of blocks. Furthermore, we show our theorems can be applied to random Gram matrices with a variance profile for which we can find the limiting spectral distributions under weaker assumptions than previous results. 

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4. The inverse scattering transform for weak Wigner–von Neumann type potentials ^*

   https://doi.org/10.1088/1361-6544/ac5f5e  

   Grudsky, Sergei; Rybkin, Alexei (April 2022, Nonlinearity)

   Abstract In the context of the Cauchy problem for the Korteweg–de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner–von Neumann type potentials with small coupling constants. Our arguments are based on the theory of Hankel operators. 

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5. The El Niño–Southern Oscillation Pattern Effect

   https://doi.org/10.1029/2021GL095261  

   Ceppi, Paulo; Fueglistaler, Stephan (October 2021, Geophysical Research Letters)

   Abstract El Niño–Southern Oscillation (ENSO) variability is accompanied by out‐of‐phase anomalies in the top‐of‐atmosphere tropical radiation budget, with anomalous downward flux (i.e., net radiative heating) before El Niño and anomalous upward flux thereafter (and vice versa for La Niña). Here, we show that these radiative anomalies result mainly from a sea surface temperature (SST) “pattern effect,” mediated by changes in tropical‐mean tropospheric stability. These stability changes are caused by SST anomalies migrating from climatologically cool to warm regions over the ENSO cycle. Our results are suggestive of a two‐way coupling between SST variability and radiation, where ENSO‐induced radiative changes may in turn feed back onto SST during ENSO. 

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