Related papers: Sharp interface limit for a phase field model in s…
This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and prove a compactness and lower bound estimate in the sharp…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a…
Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
We consider a system of two PDEs arising in modeling of motility of eukariotic cells on substrates. This system consists of the Allen-Cahn equation for the scalar phase field function coupled with another vectorial parabolic equation for…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and…
Topology optimization facilitates the automated design of high-performance structures across various engineering fields but, if unconstrained, often produces designs that are complex and difficult to manufacture. A key attribute of the…
Stacked intelligent metasurfaces (SIMs) have recently emerged as a promising metasurface-based physical-layer paradigm for wireless communications, enabling wave-domain signal processing through multiple cascaded metasurface layers.…
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
We propose a novel penalty method framework for the non-self-adjoint topology optimization problems, taking compliant mechanism problems as an example, by incorporating a convex nonlocal perimeter approximation scheme. We rigorously analyze…
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…
In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…
We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…