Related papers: Complex order-parameter phase-field models derived…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
We present a mesoscale field theory unifying the modeling of growth, elasticity, and dislocations in quasicrystals. The theory is based on the amplitudes entering their density-wave representation. We introduce a free energy functional for…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We present thermodynamic relationships between the free energy of the phase-field crystal (PFC) model and thermodynamic state variables for bulk phases under hydrostatic pressure. This relationship is derived based on the thermodynamic…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is…
A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that…
One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
Over the last few decades, phase-field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g. geometric PDEs and mean curvature flow, materials science for the study of phase transitions) but…
Chiral heteropolymers such as larger globular proteins can simultaneously support multiple length scales. The interplay between different scales brings about conformational diversity, and governs the structure of the energy landscape.…
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without well-defined order parameters remains a significant challenge. In this work, we introduce a novel…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…
Understanding the nature of brittle failure in ferroelectric materials is essential, but difficult due to the complex interaction between mechanical and electrical concentrated fields near the crack tip. In this work, an extended…
We apply the phase field crystal model to study the structure and energy of symmetric tilt grain boundaries of bcc iron in 3D. The parameters for the model are obtained by using a recently developed eight-order fitting scheme [A. Jaatinen…
Atomic-scale phase-field modeling formulates the probability densities of atomic vibrations as Gaussian distributions and derives a free energy functional using variational Gaussian theory and interatomic potentials. This framework permits…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
Three-dimensional point clouds can be viewed as discrete samples of smooth manifolds, allowing spectral analysis using the Laplace-Beltrami operator (LBO). However, the traditional point cloud manifold harmonic transform (PMHT) is limited…