Related papers: Pattern Selection in a Phase Field Model for Direc…
The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
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…
We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this…
This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid…
We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect…
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid…
We present a simple model for deep bed filtration, where particles suspended in a fluid are trapped while passing through a porous filter. A steady state of the model is reached when filter can not trap additional particles. We find the…
We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore…
Self-propelled particles that are subject to noise are a well-established generic model system for active matter. A homogeneous alignment field can be used to orient the direction of the self-propulsion velocity and to model systems like…
Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational…
In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying…