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We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where…

Soft Condensed Matter · Physics 2023-02-28 David A. Rower , Paul J. Atzberger

We consider divergence-based high order discretizations of an $L^2$-based first order system least squares formulation of a second order elliptic equation with Robin boundary conditions. For smooth geometries, we show optimal convergence…

Numerical Analysis · Mathematics 2024-08-08 Maximilian Bernkopf , Jens Markus Melenk

The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this…

Analysis of PDEs · Mathematics 2018-02-23 Shane Cooper

A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…

Numerical Analysis · Mathematics 2020-07-22 Assyr Abdulle , Doghonay Arjmand , Edoardo Paganoni

We consider the problem of finding the homogenization limit of oscillating linear elliptic equations on an arbitrary parallelizable manifold $(M,g,\Gamma)$. We replicate the concept of two-scale convergence by pulling back tensors $T$…

Analysis of PDEs · Mathematics 2024-04-22 Daniel Faraco , Luis Guijarro , Yaroslav Kurylev , Alberto Ruiz

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…

Numerical Analysis · Mathematics 2021-03-08 Assyr Abdulle , Doghonay Arjmand , Edoardo Paganoni

We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We…

Analysis of PDEs · Mathematics 2024-11-07 Hongjie Dong , Zhuolun Yang , Hanye Zhu

We study homogenisation problems for divergence form equations with rapidly sign-changing coefficients. With a focus on problems with piecewise constant, scalar coefficients in a ($d$-dimensional) crosswalk type shape, we will provide a…

Analysis of PDEs · Mathematics 2023-08-21 Marcus Waurick

This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…

Analysis of PDEs · Mathematics 2024-10-14 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…

Analysis of PDEs · Mathematics 2020-10-13 Brahim Amaziane , Leonid Pankratov , Andrey Piatnitski

Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…

Analysis of PDEs · Mathematics 2025-09-23 Shoham Sen , Yang Wang , Timothy Breitzman , Kaushik Dayal

Mixture quality plays a crucial role in the physical properties of multi-component immiscible polymer mixtures including nanocomposites and polymer blends. Such complex mixtures are often characterized by hierarchical internal structures,…

Soft Condensed Matter · Physics 2016-12-28 Yasuya Nakayama , Toshihisa Kajiwara

For a given region, and specified boundary flux and density rate of an extensive property, the optimal flux field that satisfies the balance conditions is considered. The optimization criteria are the $L^{p}$-norm and a Sobolev-like norm of…

Analysis of PDEs · Mathematics 2024-09-06 Vladimir Gol'dshtein , Reuven Segev

The aim of this paper is to adapt the notion of two-scale convergence in $L^p$ to the case of a measure converging to a singular one. We present a specific case when a thin cylinder with locally periodic rapidly oscillating boundary shrinks…

Analysis of PDEs · Mathematics 2017-03-28 Irina Pettersson

In this paper, we study internal properties of a Cosserat media. In fact, by using groupoids and smooth distributions, we obtain a three canonical equations. The \textit{non-holonomic material equation for Cosserat media} characterizes the…

Differential Geometry · Mathematics 2023-05-24 V. M. Jiménez , M. De León

We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…

Numerical Analysis · Mathematics 2025-01-08 Rong Lei

In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^{2}(0,T;H_{0}^{1}(\Omega ))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic…

Analysis of PDEs · Mathematics 2019-08-19 Tatiana Danielsson , Pernilla Johnsen

The longitudinal current density induced by the inhomogeneous electric field in the hot magnetized quark-gluon plasma has been investigated and utilized in obtaining the conductivity of the medium. The analysis has been done in the regime…

Nuclear Theory · Physics 2019-06-26 Manu Kurian , Vinod Chandra

Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…

Applied Physics · Physics 2020-11-10 Steven Psaltis , Robert Timms , Colin Please , S. Jonathan Chapman

The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this "reduced model" we prove results on…

Analysis of PDEs · Mathematics 2014-11-13 Isabell Graf , John M. Stockie