Related papers: Bifurcation Analysis Reveals Solution Structures o…
Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as…
We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes.…
Amorphization during severe plastic deformation has been observed in various crystalline materials, yet its underlying mechanisms remain poorly understood. This study introduces a novel phase-field model at the mesoscale, integrating…
We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy…
We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…
In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…
We consider phase-field models with and without lateral flow for the numerical simulation of lateral phase separation and coarsening in lipid membranes. For the numerical solution of these models, we apply an unfitted finite element method…
This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
We present a study of the structure of phase diagrams for matter-radiation systems, based on the use of coherent states and the catastrophe formalism, that compares very well with the exact quantum solutions as well as providing analytical…
The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…
We compare two recently proposed methods for the characterization of phase transitions in small systems. The usefulness of these techniques is evaluated for the case of structural transition in alanine-based peptides.
Total-reflection high-energy positron diffraction (TRHEPD) is a novel experimental method for the determination of surface structure, which has been extensively developed at the Slow Positron Facility, Institute of Materials Structure…
We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element…
We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, R\"atz, R\"oger and the second author. The model is an extended Cahn-Hilliard equation which contains…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and…