Article
Mathematics
B. Amaziane, L. Pankratov, A. Piatnitski
Summary: The paper discusses the stochastic homogenization of a system modeling immiscible compressible two-phase flow in random porous media, and successfully proves the convergence of solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mechanics
Jun-Peng Lu, Hai Mei, Liping Zu, Chenglin Ruan, Lisheng Liu, Liangliang Chu
Summary: In this study, a method based on transformation of Gaussian random fields is proposed to reconstruct the structure of general random 3D braid heterogeneous media. The reconstructed media can satisfy the explicitly determined correlation of the underlying Gaussian field as well as the microstructural information and two-point correlation function of the reference media. A robust and efficient algorithm is developed for accurate determination of the effective physical properties from local heterogeneous material. The importance of morphologically realistic microstructures is highlighted by investigating and selecting the correlation length, Gaussian complexity, representative volume element size, and mesh size. Numerical evaluations are conducted to assess the effective properties of 3D braid composites and the respective effects of the reinforcement's volume fraction and relative material parameters.
COMPOSITE STRUCTURES
(2023)
Article
Mathematics, Applied
Andro Mikelic, Andrey Piatnitski
Summary: In this paper, we study the homogenization of a system of partial differential equations in a random porous medium for the transport of an electrolyte in a solvent. We establish the convergence of the stochastic homogenization procedure and prove the well-posedness of the two-scale homogenized equations. We also demonstrate the validity of the Onsager theory for random porous media and establish the strong convergence of the fluxes.
Article
Computer Science, Theory & Methods
Jianfeng Lu, Felix Otto
Summary: The paper investigates an algorithm using multipole expansion on the boundary of a computational domain with size L to compute the solution of an elliptic coefficient field, and establishes an error estimate based on quantitative stochastic homogenization. The research shows that the prefactor can be bounded by a computable constant in the large box of given realization, with overwhelming probability.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2021)
Article
Mathematics, Applied
S. Wolf
Summary: In this paper, the homogenization of the p-Laplace equation with a periodic coefficient perturbed by a local defect is considered. The correctors are constructed and convergence results to the homogenized solution are derived in the case p > 2, assuming that the periodic correctors are non-degenerate. (c) 2022 Elsevier Ltd. All rights reserved.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Mathematics
Andrea Davini, Elena Kosygina
Summary: We prove homogenization for a class of nonconvex (possibly degenerate) viscous Hamilton-Jacobi equations in stationary ergodic random environments in one space dimension. The results concern Hamiltonians of the form G(p) + V (x, omega), where the nonlinearity G is the minimum of two or more convex functions with the same absolute minimum, and the potential V is a bounded stationary process satisfying an additional scaled hill and valley condition. This condition is trivially satisfied in the inviscid case, while it is equivalent to the original hill and valley condition of A. Yilmaz and O. Zeitouni [32] in the uniformly elliptic case. Our approach is based on PDE methods and does not rely on representation formulas for solutions. Using only comparison with suitably constructed super- and sub- solutions, we obtain tight upper and lower bounds for solutions with linear initial data x ? theta x. Another important ingredient is a general result of P. Cardaliaguet and P. E. Souganidis [13] which guarantees the existence of sublinear correctors for all theta outside flat parts of effective Hamiltonians associated with the convex functions from which G is built. We derive crucial derivative estimates for these correctors which allow us to use them as correctors for G. (c) 2022 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Theory & Methods
Nicolas Clozeau, Marc Josien, Felix Otto, Qiang Xu
Summary: This article studies the representative volume element (RVE) method, which approximates the effective behavior of a stationary random medium. The main message is to periodize the ensemble instead of its realizations, as it leads to smaller bias or systematic error. The leading-order error term is analyzed for both strategies, showing that periodizing the ensemble yields a smaller error scaling than periodizing the realization. The analysis is carried out in ensembles of Gaussian type, making use of the Price theorem and the Malliavin calculus for optimal stochastic estimates of correctors.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2023)
Article
Mechanics
Nirvana Caballero
Summary: The recent experiments demonstrate that alternating square magnetic field pulses applied to ferromagnetic samples result in a reduction in domain area and a change in domain walls roughness. This phenomenon is explained by a numerical protocol using a simple scalar-field model, which mimics the experimental findings. The observed effects are attributed to a change in disorder correlation length and the interplay between disorder effects and effective fields induced by local domain curvature.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Mechanics
Pamela C. Guruciaga, Nirvana Caballero, Vincent Jeudy, Javier Curiale, Sebastian Bustingorry
Summary: A tuned Ginzburg-Landau model is presented to study the dynamics of domain walls in thin ferromagnetic systems with perpendicular magnetic anisotropy. The model quantitatively reproduces different dynamical regimes of domain wall motion in experimental velocity-field data, while also providing detailed nano-scale information.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Acoustics
M. Colvez, R. Cottereau
Summary: This paper focuses on the modeling of elastic wave propagation at small incidence angles through a randomly-fluctuating horizontally-layered slab. The model takes into account the coupling of quasi-P and quasi-S waves by establishing a coordinate system following the coherent front. The transmission and reflection coefficients of the slab are estimated by solving a set of coupled stochastic ordinary differential equations.
Article
Multidisciplinary Sciences
Tiziano Binzoni, Alain Mazzolo
Summary: This article introduces the importance of Monte Carlo simulations in describing photon propagation in statistical mixtures, and proposes a new approach to simplify the MC approach by deriving the exact analytical expression for the probability density function of photons' random steps.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Patrick W. Dondl, Martin Jesenko
Summary: We investigate a model for the motion of a phase interface in an elastic medium, described by a semilinear parabolic equation with a fractional Laplacian. The presence of randomly distributed, localized obstacles leads to a threshold phenomenon, and a percolation result for the obstacle sites is crucial in proving the main result. Additionally, a homogenization result for such fronts in the pinning regime is derived.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Engineering, Mechanical
Zhiqiang Yang, Yi Sun, Yizhi Liu, Junzhi Cui
Summary: A novel statistical second-order reduced multiscale approach is proposed for nonlinear composite materials with random distribution of grains. This method is effective in predicting the macroscopic properties of random composite materials and has potential applications in actual engineering computation.
ACTA MECHANICA SINICA
(2021)
Article
Physics, Multidisciplinary
Joseph Pollard, Gareth P. Alexander
Summary: We provide a comprehensive topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role of chirality in the material, we demonstrate a fundamental distinction between tight and overtwisted disclination lines that is not detected by standard homotopy theory arguments. The classification of overtwisted lines is the same as nematics, but we show that tight disclinations possess a conserved topological layer number as long as the twist is nonvanishing. Additionally, we observe that chirality hinders the escape of removable defect lines and explain how this hindrance leads to the formation of several structures observed in experiments.
PHYSICAL REVIEW LETTERS
(2023)
Article
Multidisciplinary Sciences
George F. Price, Igor L. Chernyavsky, Oliver E. Jensen
Summary: We investigate the transport of solute past isolated sinks in a bounded domain dominated by advection, and evaluate the effectiveness of homogenization approximations when the sinks are randomly distributed. We find that corrections to the approximations can be non-local, non-smooth, and non-Gaussian depending on the physical parameters and the compactness of the sinks. In one dimension, solute distributions develop a staircase structure, while in two and three dimensions, they are near-singular at each sink. We approximate these corrections using a moment-expansion method and test our predictions against simulations.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
