相关论文: Step evolution in two-dimensional diblock copolyme…

In the study of equilibrium solutions for partial differential equations there are so many equilibria that one cannot hope to find them all. Therefore one usually concentrates on finding individual branches of equilibrium solutions. On the…

We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of…

The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C…

We propose a new preconditioner for the Ohta--Kawasaki equation, a nonlocal Cahn--Hilliard equation that describes the evolution of diblock copolymer melts. We devise a computable approximation to the inverse of the Schur complement of the…

Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…

We study a Phase-Field-Crystal model described by a free energy functional involving second order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $\Gamma$-convergence result in an…

In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…

Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…

It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…

Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water- and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system…

Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection of active…

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…

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 consider a phase-field model which describes the interactions between the blood flow and the thrombus. The latter is supposed to be a viscoelastic material. The potential describing the cohesive energy of the mixture is assumed to be of…

The development of complex multicellular organisms from a single parent cell is a highly orchestrated process that cells conduct collectively without central guidance, creating intricate dynamic patterns essential for development and…

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…

In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a…

In this paper, we present a phase field model for the self-climb motion of prismatic dislocation loops via vacancy pipe diffusion driven by elastic interactions. This conserved dynamics model is developed under the framework of the…

This work presents a general and unified theory describing block copolymer self-assembly in the presence of free surfaces and nanoparticles in the context of Self-Consistent Filed Theory. Specifically, the derived theory applies to free and…