Related papers: Phase field models for thin elastic structures wit…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We develop a diffuse-interface continuum model for membrane electroporation that couples a phase field for pore geometry to a quasi-static electrolyte potential and a spatially varying leaky-dielectric model for the transmembrane voltage.…
In this paper we study a constrained minimization problem for the Willmore functional. For prescribed surface area we consider smooth embeddings of the sphere into the unit ball. We evaluate the dependence of the the minimal Willmore energy…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we…
In a recent work [1] we presented results for the Bose-Fermi-Hubbard model (BFHM) in the limit of ultrafast fermions. The present work gives an overview over the used methods and an deeper insight into the implications arising from the…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
Building on work of Mondino-Scharrer, we show that among closed, smoothly embedded surfaces in $\mathbb{R}^3$ of genus $g$ and given isoperimetric ratio $v$, there exists one with minimum bending energy $\mathcal{W}$. We do this by gluing…
A general procedure is established to calculate the quantum phase diagrams for finite matter-field Hamiltonian models. The minimum energy surface associated to the different symmetries of the model is calculated as a function of the…
We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…
We study a one-dimensional interacting topological model by means of exact diagonalization method. The topological properties are firstly examined with the existence of the edge states at half-filling. We find that the topological phases…
A platform that serves as an ideal playground for realizing ``high'' temperature superconductors are materials where the electrons' kinetic energy is completely quenched, and interactions provide the only energy scale in the problem for…
Variational models for cohesive fracture are based on the idea that the fracture energy is released gradually as the crack opening grows. Recently, [Conti, Focardi, and Iurlano, Ann. Inst. H. Poincar\'e C Anal. Non Lin\'eaire, 2016]…
Diffraction of light at lateral inhomogenities is a central process in the near-field studies of nanoscale phenomena, especially the propagation of surface waves. Theoretical description of this process is extremely challenging due to…
We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence…
Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
A phase-field model for diffusion-limited crystal growth is formulated that is capable of handling highly anisotropic interfaces. It uses a Willmore regularization that yields corners of finite size. An asymptotic analysis reveals that…