Related papers: Two-well rigidity and multidimensional sharp-inter…
The numerical resolution efficiency of phase-field models is limited by grid friction, grid anisotropy and pinning. The 1D sharp phase-field model eliminates grid friction and pinning by a global restoration of Translational Invariance (TI)…
We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length $\sigma$, where the particles are confined between two parallel walls and only nearest neighbor interactions occur. As in our previous work…
The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total…
We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…
Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that…
A fluid in contact with a flat structureless wall constitutes the simplest interface system, but the fluid-wall interfacial tension cannot be trivially and even unequivocally determined due to the ambiguity in identifying the precise…
We study joining rigidity in the class of von Neumann flows with one singularity. They are given by a smooth vector field $\mathcal{X}$ on $\mathbb T^2\setminus \{a\}$, where $\mathcal{X}$ is not defined at $a\in \mathbb T^2$. It follows…
We investigate the ability of a multi-order parameter phase field model with obstacle potentials to describe grain boundary premelting in equilibrium situations. In agreement with an energetic picture we find that the transition between dry…
A parametrized double-well potential is proposed to address the issue of the impact of shape deformability of some bistable physical systems, on their quantum dynamics and classical statistical mechanics. The parametrized double-well…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
Energy functionals describing phase transitions in crystalline solids are often non-quasiconvex and minimizers might therefore not exist. On the other hand, there might be infinitely many gradient Young measures, modelling microstructures,…
The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is…
In this paper, we prove the maximal $L_p$-$L_q$ regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of ${\mathcal R}$-bounded solution operators corresponding to…
In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…
It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed…
We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial…
We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on…