相关论文: Phase-field approximation of functionals defined o…

This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…

A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed…

The Mumford-Shah functional approximates a function by a piecewise smooth function. Its versatility makes it ideal for tasks such as image segmentation or restoration, and it is now a widespread tool of image processing. Recent work has…

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type…

We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…

In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a…

We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals driven by the Caputo time-fractional derivative. Several novel…

A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…

This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…

We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.

In the phase-field modeling of brittle fracture, anisotropic constitutive assumptions for the degradation of stored elastic energy due to fracture are crucial to preventing cracking in compression and obtaining physically sound numerical…

We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while…

The paper is concerned with a posteriori estimates for approximations of boundary value problems generated by the spectral fractional Laplace operator. The derivation is based upon the Stinga--Torrea extension, which generalizes the…

The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived using a (semi-analytical) rational-function approximation method.…

Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

A crucial aspect in phase-field modeling, based on the variational formulation of brittle fracture, is the accurate representation of how the fracture surface energy is dissipated during the fracture process in the energy competition within…

It is suggested a topological hierarchical classification of the infinite many Localized phases figuring in the phase diagram of the Harper equation for anisotropy parameter $\epsilon$ versus Energy $E$ with irrational magnetic flux…

We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness constraint of (Dondl, Lemenant,…