Related papers: Convergence Relative to a Microstructure : Propert…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…
In this paper we use min-max theory to study the existence free boundary minimal hypersurfaces (FBMHs) in compact manifolds with boundary $(M^{n+1}, \partial M, g)$, where $2\leq n\leq 6$. Under the assumption that $g$ is a local maximizer…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
We study and characterize the optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form. We obtain that the optimal rate of convergence is either $O(\varepsilon)$ or $O(\varepsilon^2)$…
This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression…
We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
Material microstructures are traditionally compared using sets of statistical measures that are incomplete, e.g., two visually distinct microstructures can have identical grain size distributions and phase fractions. While this is not a…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…
We prove an upper bound for the convergence rate of the homogenization limit $\epsilon\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $\epsilon$ is a…
We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect…
We introduce the concept of nonlocal $H$-convergence. For this we employ the theory of abstract closed complexes of operators in Hilbert spaces. We show uniqueness of the nonlocal $H$-limit as well as a corresponding compactness result.…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…