Related papers: Pattern formation in vector-valued phase fields un…
Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front.…
Phase diagram of the ground states of DNA in a bad solvent is studied for a semi-flexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter $x$ and effective self-attraction promoting…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
Domain-specific constraint patterns are introduced, which form the counterpart to design patterns in software engineering for the constraint programming setting. These patterns describe the expert knowledge and best-practice solution to…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn-Hilliard model is considered as the solid phase, and only one…
The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting…
In this study, we present the phase-space analysis of Quintessence models specified by the choice of two potentials, namely the Recliner potential and what we call the broken exponential-law potential, which is a new proposal. Using a…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…
We study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. Due to the lack of strict convexity, the classical results…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators. This calls for new methods for engineering and manipulating of the vortex states. One of…
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$.…
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…
We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…
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…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of…