Related papers: A Sharp Phase Field Method
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
Computational modeling of faulting processes is an essential tool for understanding earthquake mechanics but remains challenging due to the structural and material complexities of fault zones. The phase-field method has recently enabled…
As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for…
Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the…
Recent years have witnessed significant progress in the field of neural surface reconstruction. While the extensive focus was put on volumetric and implicit approaches, a number of works have shown that explicit graphics primitives such as…
In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity…
The interfacial diffusion associated with finite volume method (FVM) discretizations of multiphase flows creates the need for an interface sharpening mechanism. Such solutions for structured quadrilateral grids are well documented, but…
In this paper we present a balanced phase field model for active surfaces. This work is devoted to the generalization of the Balanced Phase Field Model for Active Contours devised to eliminate the often undesirable curvature-dependent…
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…
The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…
In this work, we consider pressurized phase-field fracture problems in nearly and fully incompressible materials. To this end, a mixed form for the solid equations is proposed. To enhance the accuracy of the spatial discretization, a…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
This study presents an innovative direct numerical simulation approach for complex particle systems with irregular shapes and large numbers. Using partially saturated methods, it accurately models arbitrary shapes, albeit at considerable…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…