disordered media
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2022 ◽  
Vol 933 ◽  
Author(s):  
Fanli Liu ◽  
Moran Wang

We investigate the impact of wettability distribution, pore size distribution and pore geometry on the statistical behaviour of trapping in pore-throat networks during capillary displacement. Through theoretical analyses and numerical simulations, we propose and prove that the trapping patterns, defined as the percentage and distribution of trapped elements, are determined by four dimensionless control parameters. The range of all possible trapping patterns and how the patterns are dependent on the four parameters are obtained. The results help us to understand the impact of wettability and structure on trapping behaviour in disordered media.


2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Adrien Rohfritsch ◽  
Jean-Marc Conoir ◽  
Tony Valier-Brasier ◽  
Romain Pierrat ◽  
Régis Marchiano

Author(s):  
Ugur Saglam ◽  
Deniz Deger

We aim to derive a phenomenological approach to link the theories of anomalous transport governed by fractional calculus and stochastic theory with the conductivity behavior governed by the semi-empirical conductivity formalism involving Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami type conductivity equations. We want to determine the anomalous transport processes in the amorphous semiconductors and insulators by developing a theoretical approach over some mathematical instruments and methods. In this paper, we obtain an analytical expression for the average behavior of conductivity in complex or disordered media via using the fractional-stochastic differential equation, the Fourier-Laplace transform, some natural boundary-initial conditions, and familiar physical relations. We start with the stochastic equation of motion called the Langevin equation, develop its equivalent master equation called Klein-Kramers or Fokker-Planck equation, and consider the time-fractional generalization of the master equation. Once we derive the fractional master equation, then determine the expressions for the mean value of the variables or observables through some calculations and conditions. Finally, we use these expressions in the current density relation to obtain the average conductivity behavior.


Author(s):  
Junyu Sun ◽  
Jing Wang ◽  
Taotao Guo ◽  
Hua Bao ◽  
Shuxin Bai

Photonics ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 485
Author(s):  
Prabhakar Pradhan

Light wave reflection intensity from optical disordered media is associated with its phase, and the phase statistics influence the reflection statistics. A detailed numerical study is reported for the statistics of the reflection coefficient and its associated phase for plane electromagnetic waves reflected from one dimensional Gaussian white-noise optical disordered media, ranging from weak to strong disordered regimes. The full Fokker–Planck (FP) equation for the joint probability distribution in the space is simulated numerically for varying length and disorder strength of the sample; and the statistical optical transport properties are calculated. Results show the parameter regimes of the validation of the random phase approximations (RPA) or uniform phase distribution, within the Born approximation, as well as the contribution of the phase statistics to the different reflections, averaging from nonuniform phase distribution. This constitutes a complete solution for the reflection phase statistics and its effect on light transport properties in a 1D Gaussian white-noise disordered optical potential.


2021 ◽  
Author(s):  
Mohammad Rashidi ◽  
Tuomas Haggren ◽  
Zhicheng Su ◽  
Chennupati Jagadish ◽  
Sudha Mokkapati ◽  
...  

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Ran Holtzman ◽  
Marco Dentz ◽  
Ramon Planet ◽  
Jordi Ortín

2021 ◽  
Vol 15 (6) ◽  
Author(s):  
Jolanda S. Müller ◽  
Andrea Morandi ◽  
Rachel Grange ◽  
Romolo Savo

2021 ◽  
Author(s):  
Sebastian Weidemann ◽  
Mark Kremer ◽  
Stefano Longhi ◽  
Alexander Szameit

AbstractAnderson’s groundbreaking discovery that the presence of stochastic imperfections in a crystal may result in a sudden breakdown of conductivity1 revolutionized our understanding of disordered media. After stimulating decades of studies2, Anderson localization has found applications in various areas of physics3–12. A fundamental assumption in Anderson’s treatment is that no energy is exchanged with the environment. Recently, a number of studies shed new light on disordered media with dissipation14–22. In particular it has been predicted that random fluctuations solely in the dissipation, introduced by the underlying potential, could exponentially localize all eigenstates (spectral localization)14, similar to the original case without dissipation that Anderson considered. We show in theory and experiment that uncorrelated disordered dissipation can simultaneously cause spectral localization and wave spreading (dynamical delocalization). This discovery implies the breakdown of the commonly known correspondence between spectral and dynamical localization known from the Hermitian Anderson model with uncorrelated disorder.


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