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The locomotion of flexible membrane-like organisms on top of curved surfaces appears in different contexts and scales. Still, such dynamics have not yet been quantitatively modeled and no realization of such motion in manmade systems has…
We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the…
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
The recent emergence of lead-halide perovskites as active layer materials for thin film semiconductor devices including solar cells, light emitting diodes, and memristors has motivated the development of several new drift-diffusion models…
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be…
We derive effective equations of motion governing the dynamics of sharp interfaces in phase-separated binary mixtures driven by spatio-temporal modulations of their material properties. We demonstrate, in particular, that spatial…
Imbibition is a commonly encountered multiphase problem in various fields, and exact prediction of imbibition processes is a key issue for better understanding capillary flow in heterogeneous porous media. In this work, a numerical…
An interface preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving $(d-1)$-dimensional manifold directly within the $d$-dimensional mesh, which means that the interface is represented by a subset of…
We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
Grain structure plays a key role in the mechanical properties of alloy materials. Engineering the grain structure requires a comprehensive understanding of the evolution of grain boundaries (GBs) when a material is subjected to various…
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix-fracture interfaces, as well as…
We study the pore-scale transport of a conservative scalar forming an advancing mixing front, which can be re-interpreted to predict instantaneous mixing-limited bimolecular reactions. We investigate this using a set of two-dimensional,…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present…